Finite generation for valuations computing stability thresholds and applications to K-stability

no code implementations • 18 Feb 2021 • Yuchen Liu, Chenyang Xu, Ziquan Zhuang

We prove that on any log Fano pair of dimension $n$ whose stability threshold is less than $\frac{n+1}{n}$, any valuation computing the stability threshold has a finitely generated associated graded ring.

Algebraic Geometry Differential Geometry

Seshadri constants and K-stability of Fano manifolds

no code implementations • 22 Jan 2021 • Hamid Ahmadinezhad, Ziquan Zhuang

We give a lower bound of the $\delta$-invariants of ample line bundles in terms of Seshadri constants.

Algebraic Geometry