Uniform K-stability and plt blowups of log Fano pairs

Abstract

We show relationships between uniform K-stability and plt blowups of log Fano pairs. We see that it is enough to evaluate certain invariants defined by volume functions for all plt blowups in order to test uniform K-stability of log Fano pairs. We also discuss the uniform K-stability of two log Fano pairs under crepant finite covers. Moreover, we give another proof of K-semistability of the projective plane.

19 pages

Cited by in corpus (11)

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• Delta-invariants for Fano varieties with large automorphism groups
• Kähler-Einstein metrics with prescribed singularities on Fano manifolds
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• K-moduli of Fano threefolds in family 3.10
• On the continuity of Weil-Petersson volumes of the moduli space weighted points on the projective line
• On boundedness and moduli spaces of K-stable Calabi-Yau fibrations over curves