Deformation Theory

Prof. Barbara Fantechi

This is a course about infinitesimal deformation theory in algebraic geometry. Topics:

  1. Pseudocategory of Artin rings and Schlessinger functors. Infinitesimal study of schemes: étaleness, unramifiedness, smoothness.
  2. Elementary deformation theory: definition of smooth schemes, maps, vector bundles.
  3. The l.c.i. case.
  4. The general case: the cotangent complex.