Andrea Petracci (Freie Universität Berlin) - Toric geometry and singularities on K-moduli
Channel: Jesús Martínez-García
Date: 2020-12-12

Andrea Petracci (Freie Universität Berlin) - Toric geometry and singularities on K-moduli

Talk delivered at EDGE 2020 (online) Workshop "Explicit K-stability and Moduli Problems".

https://www.maths.ed.ac.uk/cheltsov/edge2020/

Abstract: An immediate consequence of Kodaira-Akizuki-Nakano vanishing is that smooth Fano varieties have unobstructed deformations. The same holds for singular Fano varieties with mild singularities and small dimension. In this talk I will show how to use the combinatorics of lattice polytopes to construct examples of K-polystable toric Fano varieties with obstructed deformations, dimension at least 3, and canonical singularities. This method produces singularities (even reducible and non-reduced) on K-moduli stacks and K-moduli spaces of Fano varieties. This is joint work with Anne-Sophie Kaloghiros.