Cycle relations on Jacobian varieties

2006/08/24 by Gerard van der Geer, van der Geer, Gerard, Alexis Kouvidakis +1
Mathematics · #14C25 #14H40 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C25 #msc:14H40

paper · pdf · doi:10.48550/arxiv.math/0608606

6 pages, latex. Appendix added with a proof by Zagier of the equivalence of Herbaut's relations and ours

arxiv created 2006/09/04 · arxiv updated 2009/12/01

Abstract

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 due to Zagier it is shown that these sets of relations are equivalent.

Related

• Algebraic cycles on the Jacobian of a curve with a g^r_d
• Relations between tautological cycles on Jacobians
• Note on curves in a Jacobian
• Tautological Cycles on Jacobian Varieties
• Universal algebraic equivalences between tautological cycles on Jacobians of curves