Deformations of Algebraic Schemes

Abstract

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.