Delta invariants of weighted hypersurfaces

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. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.