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.
Keywords
Cite
@article{arxiv.1712.07098,
title = {Extending the Double Ramification Cycle using Jacobians},
author = {David Holmes and Jesse Leo Kass and Nicola Pagani},
journal= {arXiv preprint arXiv:1712.07098},
year = {2019}
}
Comments
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)