Birationally rigid hypersurfaces

By Tommaso de Fernex. 2006

51 citations recorded by the source corpus.

We prove that for N≥4, all smooth hypersurfaces of degree N in ℙ N are birationally superrigid. First discovered in the case N=4 by Iskovskikh and Manin in a work that started this whole direction of research, this property was later conjectured to hold in general by Pukhlikov. The proof relies on the method of maximal singularities in combination with a formula on restrictions of multiplier ideals.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a6f33a4cbe2af7443bd58a6a4a9ea89d7efa4f02