Representability of codimension three cycles

TL;DR

This paper introduces a new concept for understanding codimension three cycles on fourfolds through zero cycles on surfaces, advancing the algebraic geometry theory.

Contribution

It develops the notion of representability of codimension three cycles on fourfolds via zero cycles modulo rational equivalence on surfaces.

Findings

Provides a new framework for codimension three cycle representability.

Links cycles on fourfolds to zero cycles on surfaces.

Enhances understanding of algebraic cycles and rational equivalence.

Abstract

In this paper, we develop the notion of representability of co-dimension three cycles on a fourfold in terms of zero cycles modulo rational equivalence on surfaces.