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

2017/04/30 by Spotti, Cristiano
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.00374

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.

Related

• Kähler-Einstein metrics along the smooth continuity method
• K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics
• Compact moduli space of Kahler-Einstein Fano varieties
• On the moduli of Kahler-Einstein Fano manifolds
• Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities