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# Andrea Petracci, A 1-dimensional Component of K-moduli of Del Pezzo Surfaces

## November 29, 2022 @ 5:00 pm - 6:00 pm KST

on-line

Fano varieties are algebraic varieties with positive curvature; they are basic building blocks of algebraic varieties. Great progress has been recently made by Xu et al. to construct moduli spaces of Fano varieties by using K-stability (which is related to the existence of Kähler-Einstein metrics). These moduli spaces are called K-moduli.

In this talk I will explain how to easily deduce some geometric properties of K-moduli by using toric geometry and deformation theory. In particular, I will show how to construct a 1-dimensional component of K-moduli which parametrises certain K-polystable del Pezzo surfaces.