SCHEDULE:
thursday 16-18 room M1, friday 11-13 room M4, from april 4 to april 19, with prolongation to the following week if needed.
PROGRAM (outline):
Moduli problems and deformation theory.
Infinitesimal deformations. First order deformations. Elementary examples.
Formal smoothness.
Deformations of nonsingular varieties. The local Hilbert functor. Deformations of locally free sheaves.
Functors of Artin rings. Obstruction theory of local rings and of functors of Artin rings.
Smoothness criteria and applications. Versal, semiuniversal and universal deformations.
Schlessinger's conditions.
Relation between automorphisms and existence of (semi)universal deformations. Discussion of examples.
PREREQUISITES:
Familiarity with the main notions of commutative and homological algebra and with basic language of schemes.
USEFUL REFERENCES:
R. Hartshorne: Deformation Theory, Springer GTM n. 257.
E. Sernesi: Deformations of Algebraic Schemes, Springer Grundlehren, b. 334.
NOTES FROM THE LECTURES, last update april 19, 2024.