On the Chow group of zero-cycles of Calabi-Yau hypersurfaces

TL;DR

This paper proves that for Calabi-Yau hypersurfaces in complex projective homogeneous varieties, the intersection of divisors is proportional to a point on a rational curve, establishing a canonical zero-cycle.

Contribution

It introduces a canonical zero-cycle on Calabi-Yau hypersurfaces and relates divisor intersections to points on rational curves, advancing understanding of their Chow groups.

Findings

Intersection of n divisors is proportional to a point on a rational curve

Existence of a canonical zero-cycle on Calabi-Yau hypersurfaces

Provides a new link between divisor classes and rational curves

Abstract

We prove the existence of a canonical zero-cycle on a Calabi-Yau hypersurface X in a complex projective homogeneous variety. More precisely, we show that the intersection of any n divisors on X, n=dim X, is proportional to the class of a point on a rational curve in X.