Cycles in Jacobians: infinitesimal results

Details Cycles in Jacobians: infinitesimal results Cycles in Jacobians: infinitesimal results

2012-04-19

arxiv.org/abs/1204.4410v1

Mathematics

Algebraic Geometry

Scientific paper

Let $C$ be a generic smooth curve of genus $g\geqslant 4$. We study normal functions and infinitesimal invariants associated to Ceresa cycles $W_{k}-W_{k}^{-}$, $k=2,...,g$. We show how they can be obtained from the normal function associated to the basic cycle $C-C^{-}$ and, for k=2, we also explicitely determine the zero locus of the infinitesimal invariant. For $C$ hyperelliptic of genus $g\geqslant3$, we define the $K-$theoretic counterparts of $W_{k}-W_{k}^{-}$, generalizing a construction of A. Collino, and show that they are indecomposable. We also prove the infinite generation of $CH^{3}_{ind}(J(C)\times J(C),1)$ in genus 2.

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