$K$-moduli stacks and $K$-moduli spaces are singular

Abstract: Only recently a separated moduli space for (some) Fano varieties has been constructed by several algebraic geometers: this is the $K$-moduli stack which parametrises $K$-semistable Fano varieties and has a separated good moduli space. A natural question is: are these stacks and spaces smooth? This question makes sense because deformations of smooth Fano varieties are unobstructed, so moduli stacks of smooth Fano varieties are smooth. In this talk I will explain how to use toric geometry to construct examples of non-smooth points in the $K$-moduli stack and the $K$-moduli space of Fano $3$-folds. This is joint work with Anne-Sophie Kaloghiros.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )

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Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

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