Pullbacks of Brill-Noether Classes Under Abel-Jacobi Sections

TL;DR

This paper proves that certain classes related to Brill-Noether loci, when pulled back via Abel-Jacobi sections, are contained in the tautological ring of the moduli space of stable curves, confirming a conjecture and advancing intersection theory understanding.

Contribution

It establishes that pullbacks of virtual fundamental classes of Brill-Noether loci under Abel-Jacobi sections are tautological, resolving a key conjecture in the field.

Findings

Pullbacks lie in the tautological ring of the moduli space.

Resolves a conjecture by Pagani, Ricolfi, and van Zelm.

Advances understanding of logarithmic intersection theory of ngf3n moduli spaces.

Abstract

We prove that the pullbacks of the virtual fundamental classes of the Brill-Noether loci under any Abel-Jacobi section lie in the tautological ring of the moduli space of stable curves. This resolves a conjecture of Pagani, Ricolfi and van Zelm, and is part of a broader program to understand the logarithmic intersection theory of $\Mgn$.