Infinitesimal invariants for cycles modulo algebraic equivalence and 1-cycles on Jacobians

TL;DR

This paper introduces an infinitesimal invariant for detecting algebraic equivalence of cycles in families, with applications to Jacobians and the Beauville decomposition of 1-cycles on curves.

Contribution

It constructs a new infinitesimal invariant for cycles in families, enhancing the understanding of algebraic equivalence and applying it to Jacobians and curve cycles.

Findings

Detects cycles modulo algebraic equivalence in fibers

Provides optimal results for Beauville decomposition of 1-cycles

Applies to the Ikeda family of Jacobians

Abstract

We construct an infinitesimal invariant for cycles in a family with cohomology class in the total space lying in a given level of the Leray filtration. This infinitesimal invariant detects cycles modulo algebraic equivalence in the fibers. We apply this construction to the Ikeda family, which gives optimal results for the Beauville decomposition of the 1-cycle of a very general plane curve in its Jacobian.