منابع مشابه
Infinitesimal invariants for cycles modulo algebraic equivalence and 1-cycles on Jacobians
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 i...
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We present a collection of algebraic equivalences between tautological cycles on the Jacobian J of a curve, i.e., cycles in the subring of the Chow ring of J generated by the classes of certain standard subvarieties of J . These equivalences are universal in the sense that they hold for all curves of given genus. We show also that they are compatible with the action of the Fourier transform on ...
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Let X be a smooth projective variety over an algebraically closed field k ⊂ C of characteristic zero, and Y ⊂ X a smooth complete intersection. The Weak Lefschetz theorem states that the natural restriction map H(X(C), Q) → H(Y (C), Q) on singular cohomology is an isomorphism for all i < dim(Y ). The Bloch-Beilinson conjectures on the existence of certain filtrations on Chow groups combined wit...
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We show that the direct image of the filtered logarithmic de Rham complex is a direct sum of filtered logarithmic complexes with coefficients in variations of Hodge structures, using a generalization of the decomposition theorem of Beilinson, Bernstein and Deligne to the case of filtered D-modules. As a corollary, we get the total infinitesimal invariant of a (higher) cycle in a direct sum of t...
متن کاملCurves in Jacobians to Non - Jacobians Ii
This is a second paper where we introduce deformation theory methods which can be applied to finding curves in families of principally polarized abelian varieties (ppav) containing jacobians. One of our motivations for finding interesting and computationally tractable curves in ppav is to solve the Hodge conjecture for the primitive cohomology of the theta divisor which we explain below. For ot...
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ژورنال
عنوان ژورنال: Advances in Geometry
سال: 2016
ISSN: 1615-7168,1615-715X
DOI: 10.1515/advgeom-2015-0024