The primitive cohomology of theta divisors

E. Izadi; J. Wang

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arXiv · 1410.5868

The primitive cohomology of theta divisors

E. Izadi·J. Wang

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Abstract

The primitive cohomology of the theta divisor of a principally polarized abelian variety of dimension $g$ is a Hodge structure of level $g-3$. The Hodge conjecture predicts that it is contained in the image, under the Abel-Jacobi map, of the cohomology of a family of curves in the theta divisor. We survey some of the results known about this primitive cohomology, prove a few general facts and mention some interesting open problems.

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E. Izadi, J. Wang. 2014-10-21. The primitive cohomology of theta divisors. https://arxiv.org/abs/1410.5868

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