Birational superrigidity and K-stability of singular Fano complete intersections

Abstract

We introduce an inductive argument for proving birational superrigidity and K-stability of singular Fano complete intersections of index one, using the same types of information from lower dimensions. In particular, we prove that a hypersurface in ${\mathbb{P}}^{n+1}$ of degree $n+1$ with only ordinary singularities of multiplicity at most $n-5$ is birationally superrigid and K-stable if $n\gg 0$. As part of the argument, we also establish an adjunction type result for local volumes of singularities.

Typos corrected and proofs reorganized. 15 pages. Comments welcome

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Cited by in corpus (8)

• Birational superrigidity and K-stability of Fano complete intersections of index one (with an appendix written jointly with Charlie Stibitz)
• Birational superrigidity and K-stability of singular Fano complete intersections
• Birationally rigid complete intersections of high codimension
• K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces
• Seshadri constants and K-stability of Fano manifolds
• Alpha invariants of birationally bi-rigid Fano 3-folds I
• Symmetries of Fano varieties
• On K-stability of Fano weighted hypersurfaces