Geometry Seminar

University of Tor Vergata, Department of Mathematics

8th of November 2022, 14:30-15:30, room “Dal Passo”

Speaker

Andrea Petracci

Università di Bologna

Title

Toric geometry and K-moduli of Fano varieties

Abstract

Roughly speaking, Fano varieties are the algebraic varieties with positive curvature. Very recently K-stability (i.e. the existence of Kähler-Einstein metrics) has been applied to construct moduli spaces of Fano varieties, called K-moduli.

Toric varieties are very special algebraic varieties which are constructed in a combinatorial flavour, starting from discrete objects such as polytopes.

In this talk, I would like to explain a couple of applications of the deformation theory of toric Fano varieties to the study of K-moduli spaces of Fano varieties: a) K-moduli spaces of Fano varieties can be quite singular; b) (joint work with H.Abban, I.Cheltsov, A.Kasprzyk) the K-moduli space of quartic 3-folds contains points corresponding to K-polystable varieties which are not quartic 3-folds.