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arxiv: 1204.4410 · v2 · pith:SKI7SV3Fnew · submitted 2012-04-19 · 🧮 math.AG

Cycles in Jacobians: infinitesimal results

classification 🧮 math.AG
keywords infinitesimalassociatedcyclesgenusnormalbasicceresacollino
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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-2. 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=3, we define the K-theoretic counterpart of W_{2}-W_{2}^{-}, generalizing a construction of A. Collino, and show that it is indecomposable.

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