GIT and K-stability for Fano varieties

GIT and K-stability for Fano varieties

In algebraic geometry, one studies varieties which occur as solutions to polynomial equations. In particular, we deal with projective varieties which are the solution spaces of homogeneous polynomials.

An important category of geometric objects in algebraic geometry is smooth Fano varieties, which are varieties with positive curvature. As such they can be thought of as higher dimensional analogues of the sphere. These have been classified in 1, 8 and 105 families for curves, surfaces and threefolds respectively, while in higher dimensions the number of Fano families is yet unknown, although we know that their number is bounded.

An important current problem is compactifying these families into moduli spaces, i.e., spaces which parametrise objects with some common properties. The aim for the above is so that we can study these families into more details.

In this talk Theodoros Papazachariou will discuss how one can obtain such compactifications using Geometric Invariant Theory (GIT), which studies (algebraic) group actions on varieties. Theodoros will also discuss how one can get similar compactifications using the theory of K-stability, and the links this has to GIT.

Speaker

Theodoros Papazachariou, University of Essex

How to attend

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Jesus Martinez-Garcia (jesus.martinez-garcia@essex.ac.uk)