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1.

図書
図書
1. Topics in transcendental algebraic geometry (: pbk)
edited by Phillip Griffiths
出版情報: Princeton, N.J. : Princeton University Press, 1984  viii, 316 p. ; 25 cm
シリーズ名: Annals of mathematics studies ; no. 106
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2.

図書
図書
2. A survey of the Hodge conjecture. 2nd ed
James D. Lewis
出版情報: Providence, R.I. : American Mathematical Society, c1999  xvi, 368 p. ; 26 cm
シリーズ名: CRM monograph series ; v. 10
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目次情報: 続きを見る
Complex manifolds Vector bundles Kahler manifolds Line bundles
The Lefschetz (1,1) theorem
The Lefschetz (1,1) theorem revisited
Formulation of the general Hodge conjecture
Chern class theory Cohomology of complete intersections
The Hodge theorem Analytic and topological necessities of the Kahler condition Intermediate
Jacobians Various approaches to the Hodge conjecture for varieties with well understood geometric structure
The approach to the Hodge conjecture via normal functions
Hodge theory and Chow groups Results and formulations in the singular case
A survey of the Hodge conjecture for abelian varieties Index
Index of notation
Complex manifolds Vector bundles Kahler manifolds Line bundles
The Lefschetz (1,1) theorem
The Lefschetz (1,1) theorem revisited
3.

図書
図書
3. Mixed Hodge structures and singularities (: Hardback)
Valentine S. Kulikov
出版情報: New York : Cambridge University Press, 1998  xxi, 186 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 132
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4.

図書
図書
4. Hodge decomposition : a method for solving boundary value problems
Günter Schwarz
出版情報: Berlin ; New York : Springer-Verlag, c1995  155 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1607
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5.

図書
図書
5. Introduction to Hodge theory (: pbk)
José Bertin ... [et al.] ; translated by James Lewis, Chris Peters
出版情報: Providence, R.I. : American Mathematical Society, c2002  ix, 232 p. ; 26 cm
シリーズ名: SMF/AMS texts and monographs ; vol. 8
Panoramas et synthèses ; no 3, 1996
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目次情報:
$L^2$ Hodge theory and vanishing theorems / J.-P. Demailly
Frobenius and Hodge degeneration / L. Illusie
Variations of Hodge structure, Calabi-Yau manifolds and mirror symmetry / J. Bertin ; C. Peters
$L^2$ Hodge theory and vanishing theorems / J.-P. Demailly
Frobenius and Hodge degeneration / L. Illusie
Variations of Hodge structure, Calabi-Yau manifolds and mirror symmetry / J. Bertin ; C. Peters
6.

図書
図書
6. Period mappings and period domains
James Carlson, Stefan Müller-Stach, Chris Peters
出版情報: Cambridge : Cambridge University Press, 2003  xvi, 430 p., ill. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 85
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Basic Theory of the Period Map / Part I：
Introductory examples / 1：
Cohomology of compact KÃñhler manifolds / 2：
Holomorphic invariants and cohomology / 3：
Cohomology of manifolds varying in a family / 4：
Period maps looked at infinitesimally / 5：
The Period Map: Algebraic Methods / Part II：
Spectral sequences / 6：
Koszul complexes and some applications / 7：
Further applications: Torelli theorems for hypersurfaces / 8：
Normal functions and their applications / 9：
Applications to algebraic cycles: Nori's theorem / 10：
Differential Geometric Methods / Part III：
Further differential geometric tools / 11：
Structure of period domains / 12：
Curvature estimates and applications / 13：
Harmonic maps and Hodge theory / 14：
Projective varieties and complex manifolds / Appendix A：
Homology and cohomology / Appendix B：
Vector bundles and Chern classes / Appendix C：
Basic Theory of the Period Map / Part I：
Introductory examples / 1：
Cohomology of compact KÃñhler manifolds / 2：
7.

図書
図書
7. Variations of Hodge structure of Calabi-Yau threefolds
Claire Voisin
出版情報: Roma : Scuola Normale Superiore, 1998  viii, 85 p. ; 25 cm
シリーズ名: Pubblicazioni della Classe di scienze / Scuola Normale Superiore ; Lezioni Lagrange
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8.

電子ブック
ＥＢ
8. Mixed Hodge structures (: electronic bk)
Chris A.M. Peters, Joseph H.M. Steenbrink
出版情報: [Berlin] : Springer, [20--]  1 online resource (xiii, 470 p.)
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 52
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目次情報: 続きを見る
Introduction
Basic Hodge Theory / Part I：
Compact Kahler Manifolds / 1：
Classical Hodge Theory / 1.1：
Harmonic Theory / 1.1.1：
The Hodge Decomposition / 1.1.2：
Hodge Structures in Cohomology and Homology / 1.1.3：
The Lefschetz Decomposition / 1.2：
Representation Theory of SL(2, R) / 1.2.1：
Primitive Cohomology / 1.2.2：
Applications / 1.3：
Pure Hodge Structures / 2：
Hodge Structures / 2.1：
Basic Definitions / 2.1.1：
Polarized Hodge Structures / 2.1.2：
Mumford-Tate Groups of Hodge Structures / 2.2：
Hodge Filtration and Hodge Complexes / 2.3：
Hodge to De Rham Spectral Sequence / 2.3.1：
Strong Hodge Decompositions / 2.3.2：
Hodge Complexes and Hodge Complexes of Sheaves / 2.3.3：
Refined Fundamental Classes / 2.4：
Almost Kahler V-Manifolds / 2.5：
Abstract Aspects of Mixed Hodge Structures / 3：
Introduction to Mixed Hodge Structures: Formal Aspects / 3.1：
Comparison of Filtrations / 3.2：
Mixed Hodge Structures and Mixed Hodge Complexes / 3.3：
The Mixed Cone / 3.4：
Extensions of Mixed Hodge Structures / 3.5：
Mixed Hodge Extensions / 3.5.1：
Iterated Extensions and Absolute Hodge Cohomology / 3.5.2：
Mixed Hodge structures on Cohomology Groups / Part II：
Smooth Varieties / 4：
Main Result / 4.1：
Residue Maps / 4.2：
Associated Mixed Hodge Complexes of Sheaves / 4.3：
Logarithmic Structures / 4.4：
Independence of the Compactification and Further Complements / 4.5：
Invariance / 4.5.1：
Restrictions for the Hodge Numbers / 4.5.2：
Theorem of the Fixed Part and Applications / 4.5.3：
Application to Lefschetz Pencils / 4.5.4：
Singular Varieties / 5：
Simplicial and Cubical Sets / 5.1：
Sheaves on Semi-simplicial Spaces and Their Cohomology / 5.1.1：
Cohomological Descent and Resolutions / 5.1.3：
Construction of Cubical Hyperresolutions / 5.2：
Mixed Hodge Theory for Singular Varieties / 5.3：
The Basic Construction / 5.3.1：
Mixed Hodge Theory of Proper Modifications / 5.3.2：
Restriction on the Hodge Numbers / 5.3.3：
Cup Product and the Kunneth Formula / 5.4：
Relative Cohomology / 5.5：
Construction of the Mixed Hodge Structure / 5.5.1：
Cohomology with Compact Support / 5.5.2：
Singular Varieties: Complementary Results / 6：
The Leray Filtration / 6.1：
Deleted Neighbourhoods of Algebraic Sets / 6.2：
Mixed Hodge Complexes / 6.2.1：
Products and Deleted Neighbourhoods / 6.2.2：
Semi-purity of the Link / 6.2.3：
Cup and Cap Products, and Duality / 6.3：
Duality for Cohomology with Compact Supports / 6.3.1：
The Extra-Ordinary Cup Product / 6.3.2：
Applications to Algebraic Cycles and to Singularities / 7：
The Hodge Conjectures / 7.1：
Versions for Smooth Projective Varieties / 7.1.1：
The Hodge Conjecture and the Intermediate Jacobian / 7.1.2：
A Version for Singular Varieties / 7.1.3：
Deligne Cohomology / 7.2：
Basic Properties / 7.2.1：
Cycle Classes for Deligne Cohomology / 7.2.2：
The Filtered De Rham Complex And Applications / 7.3：
The Filtered De Rham Complex / 7.3.1：
Application to Vanishing Theorems / 7.3.2：
Applications to Du Bois Singularities / 7.3.3：
Mixed Hodge Structures on Homotopy Groups / Part III：
Hodge Theory and Iterated Integrals / 8：
Some Basic Results from Homotopy Theory / 8.1：
Formulation of the Main Results / 8.2：
Loop Space Cohomology and the Homotopy De Rham Theorem / 8.3：
Iterated Integrals / 8.3.1：
Chen's Version of the De Rham Theorem / 8.3.2：
The Bar Construction / 8.3.3：
Iterated Integrals of 1-Forms / 8.3.4：
The Homotopy De Rham Theorem for the Fundamental Group / 8.4：
Mixed Hodge Structure on the Fundamental Group / 8.5：
The Sullivan Construction / 8.6：
Mixed Hodge Structures on the Higher Homotopy Groups / 8.7：
Hodge Theory and Minimal Models / 9：
Minimal Models of Differential Graded Algebras / 9.1：
Postnikov Towers and Minimal Models; the Simply Connected Case / 9.2：
Mixed Hodge Structures on the Minimal Model / 9.3：
Formality of Compact Kahler Manifolds / 9.4：
The 1-Minimal Model / 9.4.1：
The De Rham Fundamental Group / 9.4.2：
Formality / 9.4.3：
Hodge Structures and Local Systems / Part IV：
Variations of Hodge Structure / 10：
Preliminaries: Local Systems over Complex Manifolds / 10.1：
Abstract Variations of Hodge Structure / 10.2：
Big Monodromy Groups, an Application / 10.3：
Variations of Hodge Structures Coming From Smooth Families / 10.4：
Degenerations of Hodge Structures / 11：
Local Systems Acquiring Singularities / 11.1：
Connections with Logarithmic Poles / 11.1.1：
The Riemann-Hilbert Correspondence (I) / 11.1.2：
The Limit Mixed Hodge Structure on Nearby Cycle Spaces / 11.2：
Asymptotics for Variations of Hodge Structure over a Punctured Disk / 11.2.1：
Geometric Set-Up and Preliminary Reductions / 11.2.2：
The Nearby and Vanishing Cycle Functor / 11.2.3：
The Relative Logarithmic de Rham Complex and Quasi-unipotency of the Monodromy / 11.2.4：
The Complex Monodromy Weight Filtration and the Hodge Filtration / 11.2.5：
The Rational Structure / 11.2.6：
The Mixed Hodge Structure on the Limit / 11.2.7：
Geometric Consequences for Degenerations / 11.3：
Monodromy, Specialization and Wang Sequence / 11.3.1：
The Monodromy and Local Invariant Cycle Theorems / 11.3.2：
Examples / 11.4：
Applications of Asymptotic Hodge theory / 12：
Applications to Singularities / 12.1：
Localizing Nearby Cycles / 12.1.1：
A Mixed Hodge Structure on the Cohomology of Milnor Fibres / 12.1.2：
The Spectrum of Singularities / 12.1.3：
An Application to Cycles: Grothendieck's Induction Principle / 12.2：
Perverse Sheaves and D-Modules / 13：
Verdier Duality / 13.1：
Dimension / 13.1.1：
The Dualizing Complex / 13.1.2：
Statement of Verdier Duality / 13.1.3：
Extraordinary Pull Back / 13.1.4：
Perverse Complexes / 13.2：
Intersection Homology and Cohomology / 13.2.1：
Constructible and Perverse Complexes / 13.2.2：
An Example: Nearby and Vanishing Cycles / 13.2.3：
Introduction to D-Modules / 13.3：
Integrable Connections and D-Modules / 13.3.1：
From Left to Right and Vice Versa / 13.3.2：
Derived Categories of D-modules / 13.3.3：
Inverse and Direct Images / 13.3.4：
An Example: the Gauss-Manin System / 13.3.5：
Coherent D-Modules / 13.4：
Good Filtrations and Characteristic Varieties / 13.4.1：
Behaviour under Direct and Inverse Images / 13.4.3：
Filtered D-modules / 13.5：
Derived Categories / 13.5.1：
Duality / 13.5.2：
Functoriality / 13.5.3：
Holonomic D-Modules / 13.6：
Symplectic Geometry / 13.6.1：
Basics on Holonomic D-Modules / 13.6.2：
The Riemann-Hilbert Correspondence (II) / 13.6.3：
Mixed Hodge Modules / 14：
An Axiomatic Introduction / 14.1：
The Axioms / 14.1.1：
First Consequences of the Axioms / 14.1.2：
Spectral Sequences / 14.1.3：
Intersection Cohomology / 14.1.4：
The Kashiwara-Malgrange Filtration / 14.1.5：
Motivation / 14.2.1：
The Rational V-Filtration / 14.2.2：
Polarizable Hodge Modules / 14.3：
Hodge Modules / 14.3.1：
Polarizations / 14.3.2：
Lefschetz Operators and the Decomposition Theorem / 14.3.3：
Variations of Mixed Hodge Structure / 14.4：
Defining Mixed Hodge Modules / 14.4.2：
About the Axioms / 14.4.3：
Application: Vanishing Theorems / 14.4.4：
The Motivic Hodge Character and Motivic Chern Classes / 14.4.5：
Appendices / Part V：
Homological Algebra / A：
Additive and Abelian Categories / A.1：
Pre-Abelian Categories / A.1.1：
Additive Categories / A.1.2：
The Homotopy Category / A.2：
The Derived Category / A.2.2：
Injective and Projective Resolutions / A.2.3：
Derived Functors / A.2.4：
Properties of the Ext-functor / A.2.5：
Yoneda Extensions / A.2.6：
Spectral Sequences and Filtrations / A.3：
Filtrations / A.3.1：
Spectral Sequences and Exact Couples / A.3.2：
Filtrations Induce Spectral Sequences / A.3.3：
Derived Functors and Spectral Sequences / A.3.4：
Algebraic and Differential Topology / B：
Singular (Co)homology and Borel-Moore Homology / B.1：
Basic Definitions and Tools / B.1.1：
Pairings and Products / B.1.2：
Sheaf Cohomology / B.2：
The Godement Resolution and Cohomology / B.2.1：
Cohomology and Supports / B.2.2：
Cech Cohomology / B.2.3：
De Rham Theorems / B.2.4：
Direct and Inverse Images / B.2.5：
Sheaf Cohomology and Closed Subspaces / B.2.6：
Mapping Cones and Cylinders / B.2.7：
Duality Theorems on Manifolds / B.2.8：
Orientations and Fundamental Classes / B.2.9：
Local Systems and Their Cohomology / B.3：
Local Systems and Locally Constant Sheaves / B.3.1：
Homology and Cohomology / B.3.2：
Local Systems and Flat Connections / B.3.3：
Stratified Spaces and Singularities / C：
Stratified Spaces / C.1：
Pseudomanifolds / C.1.1：
Whitney Stratifications / C.1.2：
Fibrations, and the Topology of Singularities / C.2：
The Milnor Fibration / C.2.1：
Topology of One-parameter Degenerations / C.2.2：
An Example: Lefschetz Pencils / C.2.3：
References
Index of Notations
Index
Introduction
Basic Hodge Theory / Part I：
Compact Kahler Manifolds / 1：
9.

図書
図書
9. Mixed Hodge structures (: softcover)
Chris A.M. Peters, Joseph H.M. Steenbrink
出版情報: Berlin : Springer, c2008  xiii, 470 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 52
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Basic Hodge Theory / Part I：
Compact Kahler Manifolds / 1：
Classical Hodge Theory / 1.1：
Harmonic Theory / 1.1.1：
The Hodge Decomposition / 1.1.2：
Hodge Structures in Cohomology and Homology / 1.1.3：
The Lefschetz Decomposition / 1.2：
Representation Theory of SL(2, R) / 1.2.1：
Primitive Cohomology / 1.2.2：
Applications / 1.3：
Pure Hodge Structures / 2：
Hodge Structures / 2.1：
Basic Definitions / 2.1.1：
Polarized Hodge Structures / 2.1.2：
Mumford-Tate Groups of Hodge Structures / 2.2：
Hodge Filtration and Hodge Complexes / 2.3：
Hodge to De Rham Spectral Sequence / 2.3.1：
Strong Hodge Decompositions / 2.3.2：
Hodge Complexes and Hodge Complexes of Sheaves / 2.3.3：
Refined Fundamental Classes / 2.4：
Almost Kahler V-Manifolds / 2.5：
Abstract Aspects of Mixed Hodge Structures / 3：
Introduction to Mixed Hodge Structures: Formal Aspects / 3.1：
Comparison of Filtrations / 3.2：
Mixed Hodge Structures and Mixed Hodge Complexes / 3.3：
The Mixed Cone / 3.4：
Extensions of Mixed Hodge Structures / 3.5：
Mixed Hodge Extensions / 3.5.1：
Iterated Extensions and Absolute Hodge Cohomology / 3.5.2：
Mixed Hodge structures on Cohomology Groups / Part II：
Smooth Varieties / 4：
Main Result / 4.1：
Residue Maps / 4.2：
Associated Mixed Hodge Complexes of Sheaves / 4.3：
Logarithmic Structures / 4.4：
Independence of the Compactification and Further Complements / 4.5：
Invariance / 4.5.1：
Restrictions for the Hodge Numbers / 4.5.2：
Theorem of the Fixed Part and Applications / 4.5.3：
Application to Lefschetz Pencils / 4.5.4：
Singular Varieties / 5：
Simplicial and Cubical Sets / 5.1：
Sheaves on Semi-simplicial Spaces and Their Cohomology / 5.1.1：
Cohomological Descent and Resolutions / 5.1.3：
Construction of Cubical Hyperresolutions / 5.2：
Mixed Hodge Theory for Singular Varieties / 5.3：
The Basic Construction / 5.3.1：
Mixed Hodge Theory of Proper Modifications / 5.3.2：
Restriction on the Hodge Numbers / 5.3.3：
Cup Product and the Kunneth Formula / 5.4：
Relative Cohomology / 5.5：
Construction of the Mixed Hodge Structure / 5.5.1：
Cohomology with Compact Support / 5.5.2：
Singular Varieties: Complementary Results / 6：
The Leray Filtration / 6.1：
Deleted Neighbourhoods of Algebraic Sets / 6.2：
Mixed Hodge Complexes / 6.2.1：
Products and Deleted Neighbourhoods / 6.2.2：
Semi-purity of the Link / 6.2.3：
Cup and Cap Products, and Duality / 6.3：
Duality for Cohomology with Compact Supports / 6.3.1：
The Extra-Ordinary Cup Product / 6.3.2：
Applications to Algebraic Cycles and to Singularities / 7：
The Hodge Conjectures / 7.1：
Versions for Smooth Projective Varieties / 7.1.1：
The Hodge Conjecture and the Intermediate Jacobian / 7.1.2：
A Version for Singular Varieties / 7.1.3：
Deligne Cohomology / 7.2：
Basic Properties / 7.2.1：
Cycle Classes for Deligne Cohomology / 7.2.2：
The Filtered De Rham Complex And Applications / 7.3：
The Filtered De Rham Complex / 7.3.1：
Application to Vanishing Theorems / 7.3.2：
Applications to Du Bois Singularities / 7.3.3：
Mixed Hodge Structures on Homotopy Groups / Part III：
Hodge Theory and Iterated Integrals / 8：
Some Basic Results from Homotopy Theory / 8.1：
Formulation of the Main Results / 8.2：
Loop Space Cohomology and the Homotopy De Rham Theorem / 8.3：
Iterated Integrals / 8.3.1：
Chen's Version of the De Rham Theorem / 8.3.2：
The Bar Construction / 8.3.3：
Iterated Integrals of 1-Forms / 8.3.4：
The Homotopy De Rham Theorem for the Fundamental Group / 8.4：
Mixed Hodge Structure on the Fundamental Group / 8.5：
The Sullivan Construction / 8.6：
Mixed Hodge Structures on the Higher Homotopy Groups / 8.7：
Hodge Theory and Minimal Models / 9：
Minimal Models of Differential Graded Algebras / 9.1：
Postnikov Towers and Minimal Models; the Simply Connected Case / 9.2：
Mixed Hodge Structures on the Minimal Model / 9.3：
Formality of Compact Kahler Manifolds / 9.4：
The 1-Minimal Model / 9.4.1：
The De Rham Fundamental Group / 9.4.2：
Formality / 9.4.3：
Hodge Structures and Local Systems / Part IV：
Variations of Hodge Structure / 10：
Preliminaries: Local Systems over Complex Manifolds / 10.1：
Abstract Variations of Hodge Structure / 10.2：
Big Monodromy Groups, an Application / 10.3：
Variations of Hodge Structures Coming From Smooth Families / 10.4：
Degenerations of Hodge Structures / 11：
Local Systems Acquiring Singularities / 11.1：
Connections with Logarithmic Poles / 11.1.1：
The Riemann-Hilbert Correspondence (I) / 11.1.2：
The Limit Mixed Hodge Structure on Nearby Cycle Spaces / 11.2：
Asymptotics for Variations of Hodge Structure over a Punctured Disk / 11.2.1：
Geometric Set-Up and Preliminary Reductions / 11.2.2：
The Nearby and Vanishing Cycle Functor / 11.2.3：
The Relative Logarithmic de Rham Complex and Quasi-unipotency of the Monodromy / 11.2.4：
The Complex Monodromy Weight Filtration and the Hodge Filtration / 11.2.5：
The Rational Structure / 11.2.6：
The Mixed Hodge Structure on the Limit / 11.2.7：
Geometric Consequences for Degenerations / 11.3：
Monodromy, Specialization and Wang Sequence / 11.3.1：
The Monodromy and Local Invariant Cycle Theorems / 11.3.2：
Examples / 11.4：
Applications of Asymptotic Hodge theory / 12：
Applications to Singularities / 12.1：
Localizing Nearby Cycles / 12.1.1：
A Mixed Hodge Structure on the Cohomology of Milnor Fibres / 12.1.2：
The Spectrum of Singularities / 12.1.3：
An Application to Cycles: Grothendieck's Induction Principle / 12.2：
Perverse Sheaves and D-Modules / 13：
Verdier Duality / 13.1：
Dimension / 13.1.1：
The Dualizing Complex / 13.1.2：
Statement of Verdier Duality / 13.1.3：
Extraordinary Pull Back / 13.1.4：
Perverse Complexes / 13.2：
Intersection Homology and Cohomology / 13.2.1：
Constructible and Perverse Complexes / 13.2.2：
An Example: Nearby and Vanishing Cycles / 13.2.3：
Introduction to D-Modules / 13.3：
Integrable Connections and D-Modules / 13.3.1：
From Left to Right and Vice Versa / 13.3.2：
Derived Categories of D-modules / 13.3.3：
Inverse and Direct Images / 13.3.4：
An Example: the Gauss-Manin System / 13.3.5：
Coherent D-Modules / 13.4：
Good Filtrations and Characteristic Varieties / 13.4.1：
Behaviour under Direct and Inverse Images / 13.4.3：
Filtered D-modules / 13.5：
Derived Categories / 13.5.1：
Duality / 13.5.2：
Functoriality / 13.5.3：
Holonomic D-Modules / 13.6：
Symplectic Geometry / 13.6.1：
Basics on Holonomic D-Modules / 13.6.2：
The Riemann-Hilbert Correspondence (II) / 13.6.3：
Mixed Hodge Modules / 14：
An Axiomatic Introduction / 14.1：
The Axioms / 14.1.1：
First Consequences of the Axioms / 14.1.2：
Spectral Sequences / 14.1.3：
Intersection Cohomology / 14.1.4：
The Kashiwara-Malgrange Filtration / 14.1.5：
Motivation / 14.2.1：
The Rational V-Filtration / 14.2.2：
Polarizable Hodge Modules / 14.3：
Hodge Modules / 14.3.1：
Polarizations / 14.3.2：
Lefschetz Operators and the Decomposition Theorem / 14.3.3：
Variations of Mixed Hodge Structure / 14.4：
Defining Mixed Hodge Modules / 14.4.2：
About the Axioms / 14.4.3：
Application: Vanishing Theorems / 14.4.4：
The Motivic Hodge Character and Motivic Chern Classes / 14.4.5：
Appendices / Part V：
Homological Algebra / A：
Additive and Abelian Categories / A.1：
Pre-Abelian Categories / A.1.1：
Additive Categories / A.1.2：
The Homotopy Category / A.2：
The Derived Category / A.2.2：
Injective and Projective Resolutions / A.2.3：
Derived Functors / A.2.4：
Properties of the Ext-functor / A.2.5：
Yoneda Extensions / A.2.6：
Spectral Sequences and Filtrations / A.3：
Filtrations / A.3.1：
Spectral Sequences and Exact Couples / A.3.2：
Filtrations Induce Spectral Sequences / A.3.3：
Derived Functors and Spectral Sequences / A.3.4：
Algebraic and Differential Topology / B：
Singular (Co)homology and Borel-Moore Homology / B.1：
Basic Definitions and Tools / B.1.1：
Pairings and Products / B.1.2：
Sheaf Cohomology / B.2：
The Godement Resolution and Cohomology / B.2.1：
Cohomology and Supports / B.2.2：
Cech Cohomology / B.2.3：
De Rham Theorems / B.2.4：
Direct and Inverse Images / B.2.5：
Sheaf Cohomology and Closed Subspaces / B.2.6：
Mapping Cones and Cylinders / B.2.7：
Duality Theorems on Manifolds / B.2.8：
Orientations and Fundamental Classes / B.2.9：
Local Systems and Their Cohomology / B.3：
Local Systems and Locally Constant Sheaves / B.3.1：
Homology and Cohomology / B.3.2：
Local Systems and Flat Connections / B.3.3：
Stratified Spaces and Singularities / C：
Stratified Spaces / C.1：
Pseudomanifolds / C.1.1：
Whitney Stratifications / C.1.2：
Fibrations, and the Topology of Singularities / C.2：
The Milnor Fibration / C.2.1：
Topology of One-parameter Degenerations / C.2.2：
An Example: Lefschetz Pencils / C.2.3：
References
Index of Notations
Index
Introduction
Basic Hodge Theory / Part I：
Compact Kahler Manifolds / 1：
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