Birational Superrigidity and K-Stability of Singular Fano Complete Intersections

Yuchen Liu, Ziquan Zhuang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish (US)
Pages (from-to)384-403
Number of pages20
JournalInternational Mathematics Research Notices
Issue number1
StatePublished - Jan 1 2021
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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