FirstOrder Deformations

Authors: Robin Hartshorne

Publish Date: 2010

Volume: , Issue: , Pages: 5-44

PDF Link

Abstract

We start by introducing the Hilbert scheme which will be a model for the other situations and which will provide us with examples as we go along Then in Section 2 we discuss deformations over the dual numbers for Situations A B and C In Section 3 we introduce the cotangent complex and the T i functors which are needed to discuss deformations of abstract schemes Situation D in Section 5 In Section 4 we examine the special role of nonsingular varieties using the infinitesimal lifting property and the T i functors We also show that the relative notion of a smooth morphism is characterized by the vanishing of the relative T 1 functors

Keywords: