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Cycle relations on Jacobian varieties

Published online by Cambridge University Press:  17 July 2007

Gerard van der Geer  and
Alexis Kouvidakis
Gerard van der Geer
Affiliation:
Korteweg–de Vries Instituut, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands geer@science.uva.nl
Alexis Kouvidakis
Affiliation:
Department of Mathematics, University of Crete, GR-71409 Heraklion, Greece kouvid@math.uoc.gr
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Abstract

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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.

Keywords

Jacobian varietyalgebraic cycle14C2514H40
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 4 , July 2007 , pp. 900 - 908
Copyright
Foundation Compositio Mathematica 2007

Footnotes

(with an appendix by Don Zagier)