Decomposable cycles and Noether-Lefschetz loci

TL;DR

This paper demonstrates the existence of smooth degree d surfaces in projective 3-space with a high-rank group of decomposable 0-cycles, revealing new insights into algebraic cycles and their equivalence classes.

Contribution

It establishes the existence of such surfaces with a lower bound on the rank of decomposable 0-cycle groups, advancing understanding of algebraic cycle structures.

Findings

Existence of smooth degree d surfaces with high-rank decomposable 0-cycle groups

Lower bound of at least (d-1)/3 for the rank of these groups

New results on the structure of algebraic cycles in projective spaces

Abstract

We prove that there exist smooth surfaces of degree d in projective 3-space such that the group of rational equivalence classes of decomposable 0-cycles has rank at least the integer part of (d-1)/3.