Surfaces generating the even primal cohomology of an abelian fivefold

Jonathan Conder; Edward Dewey; Elham Izadi

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arXiv · 1912.10581

Surfaces generating the even primal cohomology of an abelian fivefold

Jonathan Conder·Edward Dewey·Elham Izadi

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Abstract

Given a very general abelian fivefold $A$ and a principal polarization $Θ\subset A$, we construct surfaces generating the algebraic part of the middle cohomology $H^4(Θ, {\mathbb Q})$, and determine the intersection pairing between these surfaces. In particular, we obtain a new proof of the Hodge conjecture for $H^4(Θ, {\mathbb Q})$ and show that it contains a copy of the root lattice of $E_6$.

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BibTeX RIS

Jonathan Conder, Edward Dewey, Elham Izadi. 2019-12-23. Surfaces generating the even primal cohomology of an abelian fivefold. https://arxiv.org/abs/1912.10581

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