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Algebraic cycles on the Jacobian of a curve with a linear system of given dimension

Published online by Cambridge University Press:  17 July 2007

Fabien Herbaut
Fabien Herbaut
Affiliation:
Laboratoire J. A. Dieudonné (UMR 6621 du CNRS), Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice cedex 2, France herbaut@math.unice.fr
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Abstract

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We present relations between cycles with rational coefficients modulo algebraic equivalence on the Jacobian of a curve. These relations depend on the linear systems that the curve admits. They are obtained in the tautological ring, the smallest subspace containing (an embedding of) the curve and closed under the basic operations of intersection, Pontryagin product and the pullback and pushdown induced by homotheties.

Keywords

algebraic cyclesalgebraic equivalenceslinear systemsJacobian14C1514C2014C2514K12
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 4 , July 2007 , pp. 883 - 899
Copyright
Foundation Compositio Mathematica 2007