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arXiv · 2211.04061

On the integral Hodge conjecture for real abelian threefolds

Olivier de Gaay Fortman
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Abstract

We prove the real integral Hodge conjecture for several classes of real abelian threefolds. For instance, we prove the property for real abelian threefolds $A$ whose real locus $A(\mathbb R)$ is connected, and for real abelian threefolds $A$ which are a product $A = B \times E$ of an abelian surface $B$ and an elliptic curve $E$ with connected real locus $E(\mathbb R)$. Moreover, we show that every real abelian threefold satisfies the real integral Hodge conjecture modulo torsion, and reduce the general case to the Jacobian case.

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Olivier de Gaay Fortman. 2022-11-08. On the integral Hodge conjecture for real abelian threefolds. https://arxiv.org/abs/2211.04061

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