Extending the Double Ramification Cycle using Jacobians

Abstract

We prove that the extension of the double ramification cycle defined by the first-named author (using modifications of the stack of stable curves) coincides with that defined by the last-two named authors (using an extended Brill-Noether locus on suitable compactified universal Jacobians). In particular, in the untwisted case we deduce that both of these extensions coincide with that constructed by Li and Graber-Vakil using a virtual fundamental class on a space of rubber maps.

13 pages. Supersedes the published version. 3 small changes: (1) we correct a minus sign error in what are now Formulas 19 and 21, (2) we correct the definition of [DR] in Section 2.1, and (3) we add a citation to Dudin for Lemma 8. European Journal of Mathematics (2018)

Cited by in corpus (10)

• admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves
• The moduli space of multi-scale differentials
• Double ramification cycles with target varieties
• Extending the double ramification cycle by resolving the Abel-Jacobi map
• Infinitesimal structure of the pluricanonical double ramification locus
• Pixton's formula and Abel-Jacobi theory on the Picard stack
• Pullbacks of universal Brill-Noether classes via Abel-Jacobi morphisms
• Stability conditions for line bundles on nodal curves
• Tropical double ramification loci
• Orbifold Euler Characteristics of Compactified Jacobians