Delta invariants of weighted hypersurfaces

2024/08/06 by Taro Sano, Luca Tasin, Sano, Taro +1 · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2408.03057

openalex publication_date 2024/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a lower bound for the delta invariant of the fundamental divisor of a quasi-smooth weighted hypersurface. As a consequence, we prove K-stability of a large class of quasi-smooth Fano hypersurfaces of index 1 and of all smooth Fano weighted hypersurfaces of index 1 and 2. The proofs are based on the Abban--Zhuang method and on the study of linear systems on flags of weighted hypersurfaces.

Cited by

• On the volume of K-semistable Fano manifolds
• Cohomology of hypersurfaces of weighted projective space and the intersection form on H²

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