Journal
ANNALS OF MATHEMATICS
Volume 190, Issue 2, Pages 609-656Publisher
Princeton Univ, Dept Mathematics
DOI: 10.4007/annals.2019.190.2.4
Keywords
Fano varieties; K-stability; degenerations; moduli
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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.
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