K-stability of Q-Fano Spherical Varieties via Compatible Divisors

2025/12/31 by Renpeng Zheng · 1 voice
Mathematics · #math.AG

paper · pdf

Abstract

We study the K-stability of ℚ-Fano spherical varieties using compatible divisors. More precisely, if the ℚ-Fano variety, with a reductive group action, has an open Borel subgroup orbit, then there is a unique anticanonical ℚ-divisor computing the equivariant stability threshold. This ℚ-divisor is invariant under the Borel subgroup action, and it characterizes the K-stability of a ℚ-Fano spherical variety.

Citations

• Valuative invariants for linearized line bundles on a spherical variety
• Finite generation for valuations computing stability thresholds and applications to K-stability
• A Minimizing Valuation is Quasi-monomial
• Global pluripotential theory over a trivially valued field
• Thresholds, valuations, and K-stability
• On the K-stability of Fano varieties and anticanonical divisors
• A survey on the singularities of spherical varieties
• A variational approach to the Yau-Tian-Donaldson conjecture
• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π
• Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities
• K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics
• Valuations and asymptotic invariants for sequences of ideals

Discussions

• Actually nobody. arxiv.org/abs/2601.00054 won the race among many other who hit the button at 19:00:00 UTC. But the ID assigned was 54 because ... [bsky, 3 points, 1 comments]

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