Openness of K-semistability for Fano varieties
By H. Blum, Yuchen Liu. Duke mathematical journal, 2019
120 citations recorded by the source corpus.
In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also prove that any special test configuration arises from a log canonical place of a bounded complement and establish properties of any minimizer of the stability threshold.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/410688546fd00f0b96b5781302d031fc230827d6
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- K-stability of Fano varieties: an algebro-geometric approach (2020, methodology): “ as desired. Conversely, from a weakly special test configuration Xwith an irreducible central fiber, we want to prove the induced Z-valuation vis an lc place of a Q-complement D. The original proof in [BLX19] used the cone construction. Here we gave a (simpler) global argument1, relying on some latte”
- ACC for Minimal Log Discrepancies of Exceptional Singularities (2019, unknown): “…proof [4] of the Borisov–Alexeev–Borisov conjecture, Xu’s proof [49] of the openness of K-semistability in families of log Fano pairs (see also [6]), Li’s conjecture on minimizers of the normalized volumes, and Jonsson–Musta¸tˇa’s conjecture on graded sequences of ideals which implies an…”