The rigidity theorem of Fano--Segre--Iskovskikh--Manin--Pukhlikov--Corti--Cheltsov--de Fernex--Ein--Musta\cedilla{t}\u{a}--Zhuang

TL;DR

This paper proves the superrigidity of n-dimensional smooth hypersurfaces of degree n+1, completing a century-long mathematical effort with accessible proofs based on basic algebraic geometry and vanishing theorems.

Contribution

Provides a complete, accessible proof of the superrigidity theorem for these hypersurfaces, resolving a long-standing problem in algebraic geometry.

Findings

Established superrigidity of degree n+1 hypersurfaces in projective space.

Simplified proof using basic algebraic geometry and vanishing theorems.

Completes a 100-year mathematical quest initiated by Fano.

Abstract

We prove that $n$-dimensional smooth hypersurfaces of degree $n+1$ are superrigid. Starting with the work of Fano in 1915, the proof of this Theorem took 100 years and a dozen researchers to construct. Here I give complete proofs, aiming to use only basic knowledge of algebraic geometry and some Kodaira type vanishing theorems. Version 2: many changes, especially in section 1.