Kähler-Einstein metrics on Q-smoothable Fano varieties, their moduli and some applications

Abstract

We survey recent results on the existence of Kähler-Einstein metrics on certain smoothable Fano varieties, focusing on the importance of such metrics in the construction of compact algebraic moduli spaces of K-polystable Fano varieties. Moreover, we give some applications and we discuss some natural problems which deserve future investigations.

arXiv commentThis survey is an expanded version of a talk given at the INdAM meeting "Complex and Symplectic Geometry" held in Cortona, Arezzo (Italy), 12-18 June 2016