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Cycle relations on Jacobian varieties

Published online by Cambridge University Press:  17 July 2007

Gerard van der Geer
Korteweg–de Vries Instituut, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
Alexis Kouvidakis
Department of Mathematics, University of Crete, GR-71409 Heraklion, Greece
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By using the Grothendieck–Riemann–Roch theorem we derive cycle relations modulo algebraic equivalence in the Jacobian of a curve. The relations generalize the relations found by Colombo and van Geemen and are analogous to but simpler than the relations recently found by Herbaut. In an appendix by Zagier, it is shown that these sets of relations are equivalent.

Research Article
Foundation Compositio Mathematica 2007


(with an appendix by Don Zagier)