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Surfaces generating the space of Hodge classes in the cohomology of theta divisors of dimension 4
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Elham Izadi
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ABSTRACT
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For the theta divisor of a generic principally polarized abelian variety of dimension 5, the space of degree 4 Hodge classes is of dimension 7. We produce 27 surfaces, obtained as special subvarieties for Prym structures on the abelian variety, which generate this 7-dimensional space over the rational numbers. We show that the sublattice generated by the cohomology classes of these surfaces is (up to a multiple of 2) isomorphic to the Picard lattice of a generic cubic surface. This is joint work with Jonathan Conder and Edward Dewey.
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