Rationally Equivalent Points On Hypersurfaces In ${\mathbb P}^n$

TL;DR

This paper proves a conjecture by Voisin that on a very general hypersurface of degree 2n in projective n-space, no two distinct points are rationally equivalent, highlighting a fundamental property of such hypersurfaces.

Contribution

It establishes the non-rational equivalence of distinct points on very general hypersurfaces of degree 2n, confirming Voisin's conjecture.

Findings

No two distinct points are rationally equivalent on the hypersurface.

The result applies to very general hypersurfaces of degree 2n in projective space.

It advances understanding of rational equivalence in algebraic geometry.

Abstract

We prove a conjecture of Voisin that no two distinct points on a very general hypersurface of degree $2n$ in ${\mathbb P}^n$ are rationally equivalent.