K-stability for varieties with a big anticanonical class

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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 the K-semistability condition will force them to have a klt anticanonical model, whose stability property is the same as that of the original pair.

Original languageEnglish (US)
Article number7
JournalEpijournal de Geometrie Algebrique
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology


  • K-stability
  • finite generation
  • log Fano varieties


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