Relations between tautological cycles on Jacobians
Algebraic Geometry
2007-07-09 v2
Abstract
We study tautological cycle classes on the Jacobian of a curve. We prove a new result about the ring of tautological classes on a general curve that allows, among other things, easy dimension calculations and leads to some general results about the structure of this ring. Next we obtain a vanishing result for some of the generating classes p_i; this gives an improvement of an earlier result of Herbaut. Finally we lift a result of Herbaut and van der Geer-Kouvidakis to the Chow ring (as opposed to its quotient modulo algebraic equivalence) and we give a method to obtain further explicit cycle relations. As an ingredient for this we prove a theorem about how Polishchuk's operator D lifts to the tautological subalgebra of Chow(J).
Cite
@article{arxiv.0706.3478,
title = {Relations between tautological cycles on Jacobians},
author = {Ben Moonen},
journal= {arXiv preprint arXiv:0706.3478},
year = {2007}
}