Speaker
Erroxe Etxabarri Alberdi, Mondragon Unibertsitatea
Abstract
K-stability provides a powerful algebraic notion to construct projective moduli spaces for Fano varieties, but finding explicit descriptions for specific families is still a challenge. In this talk, after a brief overview of the main definitions of K-stability, we will discuss some techniques that are used to describe these K-moduli spaces. We will look at a couple of examples of Fano three-folds with one-dimensional moduli and our new results on Family 3.3 (divisors on $\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^2$ of degree $(1,1,2)$) which has 9-dimensional moduli. This will highlight how tools like the moduli-continuity method, GIT quotients, and K3 surfaces help us classify K-polystable varieties. (Joint work with J. M. Jones and T. S. Papazachariou).