Algebraic Geometry

Geometric Invariant Theory

The modern Geometric Invariant Theory (GIT) is one of the main tools used in constructing various moduli spaces of (semi)stable coherent sheaves on projective schemes. The aim of this lecture course is to provide some basic techniques and constructions used in the application of GIT to the description of moduli spaces of sheaves.

Read more about Geometric Invariant Theory

Framed symplectic sheaves on surfaces.

Read more about Framed symplectic sheaves on surfaces.

Toric geometry

Topics:

Toric varieties: fans, the orbit-cone correspondence, completeness, resolution of singularities.
Divisors, line bundles and polytopes. Base-point free, nef and ample line bundles. Mori cone, class group, Picard group. Description in terms of polytopes.
Cohomology of coherent sheaves on toric varieties. Reflexive sheaves, differential forms, toric Serre duality, cohomology of toric divisors.

Note: 20h from February 3 to March 4 + 12h from April 4 to 14 + 8h in June