Relations between tautological cycles on Jacobians

Details Relations between tautological cycles on Jacobians Relations between tautological cycles on Jacobians

2007-06-23

arxiv.org/abs/0706.3478v2

Mathematics

Algebraic Geometry

24 pages, 2 figures. Added a conjecture of van der Geer and Kouvidakis. Corrected minor mistakes

Scientific paper

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).

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