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1.

図書

図書
Joseph L. Taylor
出版情報: Providence, R.I. : American Mathematical Society, c2002  xvi, 507 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 46
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Selected problems in one complex variable
Holomorphic functions of several variables
Local rings and varieties
The Nullstellensatz Dimension
Homological algebra Sheaves and sheaf cohomology
Coherent algebraic sheaves
Coherent analytic sheaves Stein spaces
Frechet sheaves-Cartan's theorems
Projective varieties Algebraic vs. analytic-Serre's theorems
Lie groups and their representations
Algebraic groups
The Borel-Weil-Bott theorem
Bibliography
Index
Selected problems in one complex variable
Holomorphic functions of several variables
Local rings and varieties
2.

図書

図書
Larry C. Grove
出版情報: Providence, R.I. : American Mathematical Society, c2002  x, 169 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 39
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3.

図書

図書
S. Ramanan
出版情報: Providence, R.I. : American Mathematical Society, c2005  xi, 316 p. ; 27 cm
シリーズ名: Graduate studies in mathematics ; v. 65
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Preface
Sheaves and Differential Manifolds: Definitions and Examples / Chapter 1:
Sheaves and Presheaves / 1:
Basic Constructions / 2:
Differential Manifolds / 3:
Lie Groups; Action on a Manifold / 4:
Exercises
Differential Operators / Chapter 2:
First Order Differential Operators
Locally Free Sheaves and Vector Bundles
Flow of a Vector Field
Theorem of Frobenius
Tensor Fields; Lie Derivative / 5:
The Exterior Derivative; de Rham Complex / 6:
Differential Operators of Higher Order / 7:
Integration on Differential Manifolds / Chapter 3:
Integration on a Manifold
Sheaf of Densities
Adjoints of Differential Operators
Cohomology of Sheaves and Applications / Chapter 4:
Injective Sheaves
Sheaf Cohomology
Cohomology through Other Resolutions
Singular and Sheaf Cohomologies
Cech and Sheaf Cohomologies
Differentiable Simplices; de Rham's Theorem
Connections on Principal and Vector Bundles; Lifting of Symbols / Chapter 5:
Connections in a Vector Bundle
The Space of All Connections on a Bundle
Principal Bundles
Connections on Principal Bundles
Curvature
Chern-Weil Theory
Holonomy Group; Ambrose-Singer Theorem
Linear Connections / Chapter 6:
Lifting of Symbols and Torsion
Manifolds with Additional Structures / Chapter 7:
Reduction of the Structure Group
Torsion Free G-Connections
Complex Manifolds
The Outer Gauge Group
Riemannian Geometry
Riemannian Curvature Tensor
Ricci, Scalar and Weyl Curvature Tensors
Clifford Structures and the Dirac Operator / 8:
Local Analysis of Elliptic Operators / Chapter 8:
Regularisation
A Characterisation of Densities
Schwartz Space of Functions and Densities
Fourier Transforms
Distributions
Theorem of Sobolev
Interior Regularity of Elliptic Solutions
Vanishing Theorems and Applications / Chapter 9:
Elliptic Operators on Differential Manifolds
Elliptic Complexes
Composition Formula
A Vanishing Theorem
Hodge Decomposition
Lefschetz Decomposition
Kodaira's Vanishing Theorem
The Imbedding Theorem
Appendix
Algebra
Topology
Analysis
Bibliography
Index
Preface
Sheaves and Differential Manifolds: Definitions and Examples / Chapter 1:
Sheaves and Presheaves / 1:
4.

図書

図書
Wolmer Vasconcelos
出版情報: Berlin : Springer, c2005  xii, 519 p. ; 24 cm
シリーズ名: Springer monographs in mathematics
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Preface
Introduction
Numerical Invariants of a Rees Algebra
Hilbert Functions and Multiplicities
Depth and Cohomology of Rees Algebras
Divisors of a Rees Algebra
Koszul Homology
Integral Closure of Algebras
Integral Closure and Normalization of Ideals
Integral Closure of Modules
How To
References
Notation and Terminology
Index
Preface
Introduction
Numerical Invariants of a Rees Algebra
5.

図書

図書
Fedor Bogomolov, Yuri Tschinkel, editors
出版情報: Boston : Birkhäuser, c2005  viii, 362 p. ; 25 cm
シリーズ名: Progress in mathematics ; v. 235
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6.

図書

図書
Jean-François Dat, Sascha Orlik, Michael Rapoport
出版情報: New York : Cambridge University Press, 2010  xxii, 372 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 183
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Preface
Introduction
Period Domains for GLn over Finite Fields / Part 1:
Filtered Vector Spaces / I:
Filtrations / 1:
The tensor product theorem / 2:
The Harder-Narasimhan filtration / 3:
Period Domains for GLn / II:
Definition and examples
The relation to GIT
The Harder-Narasimhan stratification
Period domains over F1 and this cells / 4:
Cohomology of Period Domains for GLn / III:
The Langlands Lemma
The generalized Steinberg representations
The Euler-Poincaré characteristic
Period Domains for Reductive Groups over Finite Fields / Part 2:
Interlude on the Tannakian Formalism / IV:
Tensor categories
Gradings and filtrations
Filtrations on Repk(G) / V:
Slopes
Semi-stability
Period Domains for Reductive Groups / VI:
Definitions
Cohomology of Period Domains for Reductive Groups / VII:
The Langlands Lemma and generalized Steinberg representations
Period Domains over p-Adic Fields / Part 3:
Filtered isocrystals / VIII:
Period domains for GLn
Isocrystals with coefficients / 5:
Period Domains for p-Adic Reductive Groups / IX:
C-isocrystals and group schemes over Isoc(L)
Filtrations on ωG
Automorphism groups and decency
Structure of X*(G)Q/G for a reductive a.g.s
Period domains
Relation to GIT / 6:
G-isocrystals with coefficients / 8:
Cohomology of Period Domains over p-Adic Fields / X:
Generalized Steinberg representations
Compactly supported l-adic cohomology of strata
The Euler-Poincaré characteristic in the basic case
Complements / Part 4:
Further Aspects of Period Domains / XI:
The fundamental complex
The relation to Deligne-Lusztig varieties
The Drinfeld space for a p-adic field
Local systems on p-adic period domains
The cohomology complex of p-adic period domains
References
Index
Preface
Introduction
Period Domains for GLn over Finite Fields / Part 1:
7.

図書

図書
Alex Kasman
出版情報: Providence, R.I. : American Mathematical Society, 2010  xvi, 304 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 54
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8.

図書

図書
H. Flenner, L. O'Carroll, W. Vogel
出版情報: New York : Springer, c1999  vi, 307 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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Introduction
Notations
The Classical Bezout Theorem / 1:
Degrees of Projective Schemes / 1.1:
Multiplicities of Local Rings / 1.2:
Joins / 1.3:
Generic Bertini Theorems / 1.4:
The Intersection Algorithm and Applications / 2:
The Intersection Algorithm / 2.1:
Application I: The Refined Bezout Theorem / 2.2:
Segre Classes, v-Cycles and Positivity / 2.3:
Segre Classes: The General Case / 2.4:
Limits of Joins and Intersections / 2.5:
Connectedness and Bertini Theorems / 3:
Connectedness Theorems / 3.1:
Applications to Intersections and Singularities of Mappings / 3.2:
Open Loci Results and the Generic Principle / 3.3:
Bertini Theorems / 3.4:
Grothendieck's Finiteness Theorem and Applications / 3.5:
A Relative Version of Krull's Principal Ideal Theorem / 3.6:
Joins and Intersections / 4:
Linear Projections / 4.1:
Tangencies of Algebraic Varieties / 4.2:
Embedded Tangent Spaces and Tangent Cones / 4.3:
Dual Varieties and the Gauss Map / 4.4:
Superadditivity of Join Defects / 4.5:
Joins, Vertices and Higher Join Varieties / 4.6:
Higher Secant Varieties of Rational Normal Scrolls / 4.7:
Converse to Bezout's Theorem / 5:
Joins of Minimal Dimension / 5.1:
A Numerical Criterion for Proper Intersection / 5.2:
The Arithmetically Cohen-Macaulay Case / 5.3:
A Local Version of Bezout's Theorem / 5.4:
Intersection Numbers and their Properties / 6:
A General Version of the j-Multiplicity / 6.1:
Intersection Numbers / 6.2:
Criteria for Bounded Multiplicity / 6.3:
Examples and Problems / 6.4:
Linkage, Koszul Cohomology and Intersections / 7:
Linkage / 7.1:
Strongly Cohen-Macaulay Subschemes / 7.2:
Linkage and the Strong Cohen-Macaulay Property / 7.3:
Applications to Cones, Joins and Secant Varieties / 7.4:
Secant Varieties for Two Dimensional Singularities / 7.5:
Limits of Joins for Small Deviation / 7.6:
Further Applications / 8:
Generic Residual Intersections / 8.1:
Generic Projections and Double Point Cycles / 8.2:
Generic Projections and the Ramification Cycle / 8.3:
Trisecant Varieties and Inner Projections / 8.4:
Appendix / A:
Some Standard Results from Commutative Algebra / A.1:
Gorenstein Rings / A.2:
Historical Remarks / A.3:
Bibliography
Index of Notations
Index
Introduction
Notations
The Classical Bezout Theorem / 1:
9.

図書

図書
Editors, Thomas Peternell, Frank-Olaf Schreyer
出版情報: Berlin : Walter de Gruyter, 2000  x, 406 p. ; 25 cm
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Almost-lines and quasi-lines on projective manifolds / Lucian Badescu ; Mauro C. Beltrametti ; Paltin Ionescu
Transfert de metrique / Daniel Barlet ; Jon Magnusson
On the classification of K3 surfaces with nine cusps / Wolf P. Barth
Complex manifolds with split tangent bundle / Arnaud Beauville
Projections from subvarieties / Alan Howard ; Michael Schneider ; Andrew J. Sommese
Generalized Petersson-Weil metric on the Douady space of embedded manifolds / Indranil Biswas ; Georg Schumacher
On simply connected Godeaux surfaces / Fabrizio Catanese ; Roberto Pignatelli
On the Wahl map of plane nodal curves / Ciro Ciliberto ; Angelo Felice Lopez ; Rick Miranda
A remark on projective embeddings of varieties with non-negative cotangent bundles / Lawrence Ein ; Bo Ilic ; Robert Lazarsfeld
The fundamental group's structure of the complement of some configurations of real line arrangements / David Garber ; Mina Teicher
Kahlerian structures on symplectic reductions / Peter Heinzner ; Alan Huckleberry
Nef divisors on moduli spaces of abelian varieties / Klaus Hulek
Abelian surfaces with two plane cubic curve fibrations and Calabi-Yau threefolds / Kristian Ranestad
Real algebraic threefolds IV. Del Pezzo fibrations / Janos Kollar
Seiberg-Witten invariants for 4-manifolds with b+ = 0 / Christian Okonek ; Andrei Teleman
A geometric proof of Ax' theorem / Jeroen G. Spandaw
A note on the Cayley-Bacharach property for vector bundles / Sheng-Li Tan ; Eckart Viehweg
The scientific work of Michael Schneider / Thomas Peternell
Michael Schneider-an alpine vita / Ulf Persson
Lectures of the Symposium
List of Authors and Participants
Almost-lines and quasi-lines on projective manifolds / Lucian Badescu ; Mauro C. Beltrametti ; Paltin Ionescu
Transfert de metrique / Daniel Barlet ; Jon Magnusson
On the classification of K3 surfaces with nine cusps / Wolf P. Barth
10.

図書

図書
A.N. Parshin, I.R. Shafarevich (eds.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1999  247 p. ; 25 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 47 . Algebraic geometry ; 5
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