Birationally rigid Fano threefold hypersurfaces

TL;DR

This paper proves that all quasi-smooth hypersurfaces within 95 families of weighted Fano threefold hypersurfaces are birationally rigid, establishing a significant classification result in algebraic geometry.

Contribution

It demonstrates the birational rigidity of a large class of weighted Fano threefold hypersurfaces, extending the understanding of their birational properties.

Findings

All hypersurfaces in the 95 families are birationally rigid.

The result applies to quasi-smooth hypersurfaces.

It advances classification of Fano threefolds.

Abstract

We prove that every quasi-smooth hypersurface in the 95 families of weighted Fano threefold hypersurfaces is birationally rigid.