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. Further 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 lifts to the tautological subalgebra of CH(J).
Cite this article
Ben Moonen, Relations between tautological cycles on Jacobians. Comment. Math. Helv. 84 (2009), no. 3, pp. 471–502DOI 10.4171/CMH/170