We prove that K-polystable degenerations of ℚ -Fano varieties are unique. Furthermore, we show that the moduli stack of K-stable ℚ-Fano varieties is separated. Together with recently proven boundedness and openness statements, the latter result yields a separated Deligne-Mumford stack parametrizing all uniformly K-stable ℚ-Fano varieties of fixed dimension and volume. The result also implies that the automorphism group of a K-stable ℚ-Fano variety is finite.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Fano varieties