# K-stability of finite covers

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Ruadhai Dervan

created by risa on 19 Mar 2015

26 mar 2015
-- 14:45

Aula 211, Dip. Matematica, Università "Roma Tre", Roma

**Abstract.**

A conjecture of Yau, Tian and Donaldson is that the existence of a
canonical Kahler metric on an ample line bundle L over projective
variety X should be equivalent to K-stability, an algebro-geometric
notion which is closely related to Geometry Invariant Theory. However,
K-stability is understood in very few specific cases. Given a K-stable
Fano variety X, we show that certain finite covers of X are also
K-stable, giving algebro-geometric proofs of K-stability in several
new examples.