K-moduli of Fano threefolds of Picard rank 3 and degree 20

Elena Denisova (University of Glasgow)

Wednesday 18th March 16:00-17:00
Maths 311B

Abstract

(Joint work in progress with T. Papazachariou)
K-moduli spaces provide a canonical parametrization of K-polystable Fano varieties, but they are rarely accessible in concrete terms. In this talk I will describe an explicit example in dimension three. I will consider the Fano threefolds in Mori-Mukai family no. 3.5, which can be realised as blow-ups of P1xP2 along curves of bidegree (5,2). I will explain how the K-stability of these threefolds is determined by the classical GIT stability of the corresponding curves. This leads to an explicit description of the K-moduli space as a GIT quotient and yields a K-classification of all members of the family.

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