On the integral Hodge conjecture for real abelian threefolds

authored by

Olivier De Gaay Fortman

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 whose real locus is connected, and for real abelian threefolds A which are the product A = B × E of an abelian surface B and an elliptic curve E with connected real locus E (R). Moreover, we show that every real abelian threefold satisfies the real integral Hodge conjecture modulo torsion, and reduce the principally polarized case to the Jacobian case.

Organisation(s)

Institute of Algebraic Geometry

Type

Article

Journal

Journal fur die Reine und Angewandte Mathematik

Volume

2024

Pages

221-255

No. of pages

35

ISSN

0075-4102

Publication date

01.02.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

General Mathematics, Applied Mathematics

Electronic version(s)

https://doi.org/10.1515/crelle-2023-0082 (Access: Closed)