KASS seminar

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.