Pullbacks of universal Brill-Noether classes via Abel-Jacobi morphisms

Abstract

Following Mumford and Chiodo, we compute the Chern character of the derived pushforward $\text{ch}(R^{\bullet }{\pi }_{\ast }\mathcal{O}(\mathsf{D}))$, for $\mathsf{D}$ an arbitrary element of the Picard group of the universal curve over the moduli stack of stable marked curves. This allows us to express the pullback of universal Brill-Noether classes via Abel-Jacobi sections to the compactified universal Jacobians, for all compactifications such that the section is a well-defined morphism.

Major rewrite to Sections 1 and 2 due to an error (now fixed) in the main formula of v1. Added a section on the relation with the double ramification cycle. Third author joined

References in corpus (3)

• The stability space of compactified universal Jacobians
• Extending the double ramification cycle by resolving the Abel-Jacobi map
• Extending the Double Ramification Cycle using Jacobians

Cited by in corpus (1)

• admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves