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1.

図書

図書
by J.L.S. Hatton
出版情報: Cambridge : At the University Press, 1920  vi, 215 p. ; 24 cm
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2.

図書

図書
A.F. Beardon
出版情報: Chichester [Eng.] ; New York : Wiley, c1979  xiii, 239 p. ; 23 cm
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3.

図書

図書
A. I. Markushevich
出版情報: Delhi : Hindustan Publishing Corpn., 1961  62 p ; 23 cm
シリーズ名: International monographs on advanced mathematics and physics
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4.

図書

図書
Theral O. Moore and Edwin H. Hadlock
出版情報: Singapore : World Scientific, c1991  x, 391 p. ; 23 cm
シリーズ名: Series in pure mathematics ; v. 9
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5.

図書

図書
by I. M. Yaglom ; translated by Eric J. F. Primrose
出版情報: New York : Academic Press, 1968  xii, 243 p. ; 21 cm
シリーズ名: Academic paperbacks
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6.

図書

図書
Donu Arapura
出版情報: New York : Springer, c2012  xii, 329 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Preface
Introduction through Examples / Part I:
Plane Curves / 1:
Conics / 1.1:
Singularities / 1.2:
Bézout's Theorem / 1.3:
Cubics / 1.4:
Genus 2 and 3 / 1.5:
Hyperelliptic Curves / 1.6:
Sheaves and Geometry / Part II:
Manifolds and Varieties via Sheaves / 2:
Sheaves of Functions / 2.1:
Manifolds / 2.2:
Affine Varieties / 2.3:
Algebraic Varieties / 2.4:
Stalks and Tangent Spaces / 2.5:
1-Forms, Vector Fields, and Bundles / 2.6:
Compact Complex Manifolds and Varieties / 2.7:
More Sheaf Theory / 3:
The Category of Sheaves / 3.1:
Exact Sequences / 3.2:
Affine Schemes / 3.3:
Schemes and Gluing / 3.4:
Sheaves of Modules / 3.5:
Line Bundles on Projective Space / 3.6:
Direct and Inverse Images / 3.7:
Differentials / 3.8:
Sheaf Cohomology / 4:
Flasque Sheaves / 4.1:
Cohomology / 4.2:
Soft Sheaves / 4.3:
C-Modules Are Soft / 4.4:
Mayer-Vietoris Sequence / 4.5:
Products* / 4.6:
De Rham Cohomology of Manifolds / 5:
Acyclic Resolutions / 5.1:
De Rham's Theorem / 5.2:
Künneth's Formula / 5.3:
Poincaré Duality / 5.4:
Gysin Maps / 5.5:
Projections / 5.5.1:
Inclusions / 5.5.2:
Fundamental Class / 5.6:
Lefschetz Trace Formula / 5.7:
Riemann Surfaces / 6:
Genus / 6.1:
∂-Cohomology / 6.2:
Projective Embeddings / 6.3:
Function Fields and Automorphisms / 6.4:
Modular Forms and Curves / 6.5:
Simphicial Methods / 7:
Simplicial and Singular Cohomology / 7.1:
Cohomology of Projective Space / 7.2:
Cech Cohomology / 7.3:
Cech Versus Sheaf Cohomology / 7.4:
First Chern Class / 7.5:
Hodge Theory / Part III:
The Hodge Theorem for Riemannian Manifolds / 8:
Hodge Theory on a Simplicial Complex / 8.1:
Harmonic Forms / 8.2:
The Heat Equation* / 8.3:
Toward Hodge Theory for Complex Manifolds / 9:
Riemann Surfaces Revisited / 9.1:
Dolbeault's Theorem / 9.2:
Complex Tori / 9.3:
Kähler Manifolds / 10:
Kähler Metrics / 10.1:
The Hodge Decomposition / 10.2:
Picard Groups / 10.3:
A Little Algebraic Surface Theory / 11:
Examples / 11.1:
The Neron-Severi Group / 11.2:
Adjunction and Riemann-Roch / 11.3:
The Hodge Index Theorem / 11.4:
Fibered Surfaces* / 11.5:
Hodge Structures and Homological Methods / 12:
Pure Hodge Structures / 12.1:
Canonical Hodge Decomposition / 12.2:
Hodge Decomposition for Moishezon Manifolds / 12.3:
Hypercohomology* / 12.4:
Holomorphic de Rham Complex* / 12.5:
The Deligne-Hodge Decomposition* / 12.6:
Topology of Families / 13:
Topology of Families of Elliptic Curves / 13.1:
Local Systems / 13.2:
Higher Direct Images* / 13.3:
First Betti Number of a Fibered Variety* / 13.4:
The Hard Lefschetz Theorem / 14:
Hard Lefschetz / 14.1:
Proof of Hard Lefschetz / 14.2:
Weak Lefschetz and Barth's Theorem / 14.3:
Lefschetz Pencils* / 14.4:
Cohomology of Smooth Projective Maps* / 14.5:
Coherent Cohomology / Part IV:
Coherent Sheaves / 15:
Coherence on Ringed Spaces / 15.1:
Coherent Sheaves on Affine Schemes / 15.2:
Coherent Sheaves on Pn / 15.3:
GAGA, Part I / 15.4:
Cohomology of Coherent Sheaves / 16:
Cohomology of Affine Schemes / 16.1:
Cohomology of Coherent Sheaves on Pn / 16.2:
Cohomology of Analytic Sheaves / 16.3:
GAGA, Part II / 16.4:
Computation of Some Hodge Numbers / 17:
Hodge Numbers of Pn / 17.1:
Hodge Numbers of a Hypersurface / 17.2:
Hodge Numbers of a Hypersurface II / 17.3:
Double Covers / 17.4:
Griffiths Residues* / 17.5:
Deformations and Hodge Theory / 18:
Families of Varieties via Schemes / 18.1:
Semicontinuity of Coherent Cohomology / 18.2:
Deformation Invariance of Hodge Numbers / 18.3:
Noether-Lefschetz* / 18.4:
Analogies and Conjectures* / Part V:
Analogies and Conjectures / 19:
Counting Points and Euler Characteristics / 19.1:
The Weil Conjectures / 19.2:
A Transcendental Analogue of Weil's Conjecture / 19.3:
Conjectures of Grothendieck and Hodge / 19.4:
Problem of Computability / 19.5:
Hodge Theory without Analysis / 19.6:
References
Index
Preface
Introduction through Examples / Part I:
Plane Curves / 1:
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