Deformations of algebraic schemes
"This self-contained account of deformation theory in classical algebraic geometry (over an algebraically closed field) brings together for the first time some results previously scattered in the literature, with proofs that are relatively little known, yet of everyday relevance to algebraic geometers. It includes applications to the construction and properties of Severi varieties of families of plane nodal curves, space curves, deformations of quotient singularities, Hilbert schemes of points, local Picard functors, etc. Many examples are provided. The style of exposition is kept at a level amenable to graduate students with an average background in algebraic geometry."--Jacket
Springer eBooks
1 online resource (xi, 339 pages)
9783540306085, 9783540306153, 9781280853265, 9786610853267, 3540306080, 3540306153, 1280853263, 6610853266
159935056
Introduction
Infinitesimal Deformations: Extensions. Locally Trivial Deformations
Formal Deformation Theory: Obstructions. Extensions of Schemes. Functors of Artin Rings. The Theorem of Schlessinger. The Local Moduli Functors
Formal Versus Algebraic Deformations. Automorphisms and Prorepresentability
Examples of Deformation Functors: Affine Schemes. Closed Subschemes. Invertible Sheaves. Morphisms
Hilbert and Quot Schemes: Castelnuovo-Mumford Regularity. Flatness in the Projective Case. Hilbert Schemes. Quot Schemes. Flag Hilbert Schemes. Examples and Applications. Plane Curves
Appendices: Flatness. Differentials. Smoothness. Complete Intersections. Functorial Language
List of Symbols
Bibliography
English
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