Delta invariants of weighted hypersurfaces

TL;DR

This paper establishes lower bounds for delta invariants of weighted hypersurfaces, leading to new results on their K-stability, especially for Fano hypersurfaces of low index, using advanced algebraic geometry techniques.

Contribution

It provides new lower bounds for delta invariants of weighted hypersurfaces and proves K-stability for a broad class of Fano hypersurfaces of low index.

Findings

Proved K-stability of many quasi-smooth Fano hypersurfaces of index 1.

Established lower bounds for delta invariants of weighted hypersurfaces.

Applied Abban--Zhuang method and linear systems analysis on flags.

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.