Infinitesimal invariants for cycles modulo algebraic equivalence and 1-cycles on Jacobians | Zendy

Claire Voisin | Zendy

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Infinitesimal invariants for cycles modulo algebraic equivalence and 1-cycles on Jacobians

Author(s) -

Claire Voisin

Publication year - 2014

Publication title -

algebraic geometry

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.563

H-Index - 20

eISSN - 2214-2584

pISSN - 2313-1691

DOI - 10.14231/ag-2014-008

Subject(s) - modulo , infinitesimal , equivalence (formal languages) , mathematics , algebraic number , algebra over a field , pure mathematics , arithmetic , discrete mathematics , mathematical analysis

We construct an infinitesimal invariant for cycles in a family with cohomology class in the total space lying in a given level of the Leray filtration. This infinitesimal invariant detects cycles modulo algebraic equivalence in the fibers. We apply this construction to the Ikeda family, which gives optimal results for the Beauville decomposition of the 1-cycle of a very general plane curve in its Jacobian.

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