Elena Denisova: On K-stability of Fano threefolds of Picard rank 1 and genus 12. (joint work with Anne-Sophie Kaloghiros

Speaker
Elena Denisova, University of Glasgow

Abstract
This talk focuses on the existence of Kahler-Einstein metrics on Fano varieties. While such metrics always exist on general type and Calabi-Yau varieties, the situation for Fano varieties is more delicate. The key result is that the existence of a Kahler-Einstein metric on a Fano variety is equivalent to an algebro-geometric condition called K-polystability (Yau-Tian-Donaldson conjecture). This conjecture has been proven in increasing generality over the past decade. We focus on a specific family: Fano threefolds of Picard rank 1 and genus 12. A full characterization of their stability remains open. Building on Prokhorov’s classification of their one-nodal degenerations into four families, we show that the general member of each such family is K-polystable.