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.
Original language | English (US) |
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Pages (from-to) | 384-403 |
Number of pages | 20 |
Journal | International Mathematics Research Notices |
Volume | 2021 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 2021 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)