JournalscmhVol. 84 , No. 3DOI 10.4171/cmh/170

Relations between tautological cycles on Jacobians

  • Ben Moonen

    University of Amsterdam, Netherlands
Relations between tautological cycles on Jacobians cover

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. 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 D\mathcal{D} lifts to the tautological subalgebra of CH(J).