Deformations of singular varieties

Lectures by Prof. Barbara Fantechi (SISSA) at the Research Institute for Mathematical Sciences (RIMS), Kyoto University, April 13–14, 2026.

Lecture 1

After briefly reviewing functors over Artinian algebras (over a fixed algebraically closed field) we focus on deformations of singular varieties, and in particular those which have lci singularities.

1A 1B 1C 1D 1E 1F 1G 1H 1I 1J

Lecture 2

We review Tziolas’s result on formal smoothability, describe applications to smoothening of stable surfaces (joint work with Franciosi and Pardini) and a similar, independent smoothability result (joint with Miró Roig).

2A 2B 2C 2D 2E 2F 2G 2H 2I 2J 2K 2L 2M

Lecture 3

We relate what done so far with algebraic stacks and complex analytic geometry; if time allows we discuss work in progress with Siao Chi Mok on the stack of Fulton-MacPherson expansions.

3A 3B 3C 3D 3E 3F 3G 3H 3I 3J 3K 3L 3M 3N 3O 3P