K-stability for varieties with a big anticanonical class

Abstract

We extend the algebraic K-stability theory to projective klt pairs with a big anticanonical class. While in general such a pair could behave pathologically, it is observed in this note that K-semistability condition will force them to have a klt anticanonical model, whose stability property is the same as the original pair.

9 pages, Final version

References in corpus (3)

• Stable degenerations of singularities
• Ding stability and Kähler-Einstein metrics on manifolds with big anticanonical class
• Twisted Kähler-Einstein metrics in big classes