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1.

図書

図書
Freddy Van Oystaeyen
出版情報: New York : Marcel Dekker, c2000  vi, 287 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 232
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2.

図書

図書
I.R. Shafarevich (ed.)
出版情報: Berlin ; New York : Springer-Verlag, c1994  307 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 23 . Algebraic geometry ; 1
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目次情報:
Riemann Surfaces and Algebraic Curves / V.V. Shokurov
Algebraic Varieties and Schemes / V.I. Danilov
Riemann Surfaces and Algebraic Curves / V.V. Shokurov
Algebraic Varieties and Schemes / V.I. Danilov
3.

図書

図書
by Eric M. Friedlander
出版情報: Princeton, N.J. : Princeton University Press, 1982  vii, 190 p. ; 25 cm
シリーズ名: Annals of mathematics studies ; no. 104
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4.

図書

図書
[by] Alexandre Grothendieck [and] Jacob P. Murre
出版情報: Berlin ; New York : Springer-Verlag, 1971  viii, 133 p. ; 26 cm
シリーズ名: Lecture notes in mathematics ; 208
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5.

図書

図書
I.G. Macdonald
出版情報: New York : W.A. Benjamin, 1968  vii, 113 p. ; 23-24 cm
シリーズ名: Mathematics lecture note series
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6.

図書

図書
Edoardo Sernesi
出版情報: Berlin : Springer, c2006  xi, 339 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 334
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目次情報: 続きを見る
Terminology and notation
Introduction
Infinitesimal deformations / 1:
Extensions / 1.1:
Generalities / 1.1.1:
Extensions of schemes / 1.1.2:
Locally trivial deformations / 1.2:
Generalities on deformations / 1.2.1:
Infinitesimal deformations of nonsingular affine schemes / 1.2.2:
Extending automorphisms of deformations / 1.2.3:
First-order locally trivial deformations / 1.2.4:
Higher-order deformations - obstructions / 1.2.5:
Formal deformation theory / 2:
Obstructions / 2.1:
Functors of Artin rings / 2.2:
The theorem of Schlessinger / 2.3:
The local moduli functors / 2.4:
Obstruction spaces / 2.4.1:
Algebraic surfaces / 2.4.3:
Formal versus algebraic deformations / 2.5:
Automorphisms and prorepresentability / 2.6:
The automorphism functor / 2.6.1:
Isotriviality / 2.6.2:
Examples of deformation functors / 3:
Affine schemes / 3.1:
First-order deformations / 3.1.1:
The second cotangent module and obstructions / 3.1.2:
Comparison with deformations of the nonsingular locus / 3.1.3:
Quotient singularities / 3.1.4:
Closed subschemes / 3.2:
The local Hilbert functor / 3.2.1:
The forgetful morphism / 3.2.2:
The local relative Hilbert functor / 3.2.4:
Invertible sheaves / 3.3:
The local Picard functors / 3.3.1:
Deformations of sections, I / 3.3.2:
Deformations of pairs (X, L) / 3.3.3:
Deformations of sections, II / 3.3.4:
Morphisms / 3.4:
Deformations of a morphism leaving domain and target fixed / 3.4.1:
Deformations of a morphism leaving the target fixed / 3.4.2:
Morphisms from a nonsingular curve with fixed target / 3.4.3:
Deformations of a closed embedding / 3.4.4:
Stability and costability / 3.4.5:
Hilbert and Quot schemes / 4:
Castelnuovo-Mumford regularity / 4.1:
Flatness in the projective case / 4.2:
Flatness and Hilbert polynomials / 4.2.1:
Stratifications / 4.2.2:
Flattening stratifications / 4.2.3:
Hilbert schemes / 4.3:
Linear systems / 4.3.1:
Grassmannians / 4.3.3:
Existence / 4.3.4:
Quot schemes / 4.4:
Local properties / 4.4.1:
Flag Hilbert schemes / 4.5:
Examples and applications / 4.5.1:
Complete intersections / 4.6.1:
An obstructed (nonreduced) scheme / 4.6.2:
Relative grassmannians and projective bundles / 4.6.4:
Hilbert schemes of points / 4.6.5:
Schemes of morphisms / 4.6.6:
Focal loci / 4.6.7:
Plane curves / 4.7:
Equisingular infinitesimal deformations / 4.7.1:
The Severi varieties / 4.7.2:
Nonemptiness of Severi varieties / 4.7.3:
Flatness / A:
Differentials / B:
Smoothness / C:
Regular embeddings / D:
Relative complete intersection morphisms / D.2:
Functorial language / E:
References
List of symbols
Index
Terminology and notation
Introduction
Infinitesimal deformations / 1:
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