Event time:
Thursday, February 23, 2017 - 10:00am to 11:00am
Location:
431 DL
Speaker:
Yuchen Liu
Speaker affiliation:
Princeton University
Event description:
A complex projective variety is Q-Fano if it has klt singularities and the anti-canonical divisor is Q-Cartier and ample. Starting from dimension 2, the anti-canonical volume of a Q-Fano variety can be arbitrarily large, e.g. weighted projective spaces. Recently, Fujita showed that projective spaces have maximal volume among K\ahler-Einstein Q-Fano varieties. In this talk, I will discuss a refinement of Fujita’s volume upper bounds involving invariants of the local singularities. If time permits, I will also talk about an equivalent relation between K-semistability and de Fernex-Ein-Mustata type inequalities. Part of this work is joint with Chi Li.