On divisorial stability of finite covers

Abstract: Divisorial stability of a polarised variety is a stronger - but conjecturally equivalent - variant of uniform K-stability introduced by Boucksom-Jonsson. Whereas uniform K-stability is defined in terms of test configurations, divisorial stability is defined in terms of convex combinations of divisorial valuations on the variety. In this talk, I will give a quick account on divisorial stability, and then I will describe the behaviour of divisorial stability under finite group actions. In particular, I will show that equivariant divisorial stability of a polarised variety is equivalent to log divisorial stability of its quotient. I will then use this result to give a general construction of equivariantly divisorially stable polarised varieties. This is joint work with R. Dervan.

algebraic geometrycombinatorics

Audience: researchers in the topic

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