Algebraic and Arithmetic Geometry Seminar
# Singularities on K-moduli spaces of Fano varieties

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Europe/Rome

Aula Mancini (SNS)
### Aula Mancini

#### SNS

Description

Recently there has been spectacular progress, due to many scholars, on the construction of moduli (called K-moduli) of Fano varieties using K-stability (which is related to the existence of Kähler-Einstein metrics). It is a natural question to understand the geometry of these (newly constructed) spaces. Although smooth Fano varieties have unobstructed deformations, in joint work with Kaloghiros we constructed the first examples of obstructed K-polystable Fano varieties by using toric geometry. These give singular points on K-moduli of Fanos. In this talk I will try to explain these constructions; as a corollary I will show that K-moduli of Fano of dimension at least 3 can have arbitrarily many local branches.