Talk page
Title:
Valuations and stability of polarised varieties
Speaker:
Abstract:
The valuative approach to the theory of K-stability of Fano varieties has led to many recent advances, for example to the construction of moduli spaces of Fano varieties. I will survey how valuations can be used to study K-stability of general polarised varieties, namely projective varieties endowed with an ample line bundle. I will begin by describing work of myself and Legendre defining a stability condition (“valuative stability”) using divisorial valuations, and will then describe work of Boucksom-Jonsson defining a stability condition (“divisorial stability”) using convex combinations of divisorial valuations. While valuative stability should only be expected to capture K-stability in the Fano setting (and should be strictly weaker in general), divisorial stability is conjectured to be equivalent to (uniform) K-stability for general polarised varieties. I will describe some applications of this new valuative approach: openness of the divisorially stable locus in the ample cone (Boucksom-Jonsson) and a description of the behaviour of divisorial stability under finite covers (joint work with Papazachariou).
Link:
Workshop: