On the integral Hodge conjecture for real abelian threefolds
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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
Funding statement: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754362.
Acknowledgements
This paper is based on results that appear in the last chapter of my PhD thesis [12]. I thank my advisor Olivier Benoist for the great guidance he has given me over the past three years. In particular, I owe him much for drawing my attention to the real integral Hodge conjecture, and for the many discussions we had concerning this project. I thank Nicolas Tholozan for several discussions on moduli of real abelian varieties, and in particular for explaining to me how to prove Theorem 1.5. Moreover, I thank Fabrizio Catanese, François Charles and Javier Fresán for stimulating conversations, and I thank Olivier Benoist and Olivier Wittenberg for useful comments on an earlier version of this paper.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Singular set and curvature blow-up rate of the level set flow
- Counting integral points of bounded height on varieties with large fundamental group
- 𝔸1-connected components and characterisation of 𝔸2
- New phenomena in deviation of Birkhoff integrals for locally Hamiltonian flows
- Torus counting and self-joinings of Kleinian groups
- Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments
- On the integral Hodge conjecture for real abelian threefolds
- Weakly Kähler hyperbolic manifolds and the Green–Griffiths–Lang conjecture
Articles in the same Issue
- Frontmatter
- Singular set and curvature blow-up rate of the level set flow
- Counting integral points of bounded height on varieties with large fundamental group
- 𝔸1-connected components and characterisation of 𝔸2
- New phenomena in deviation of Birkhoff integrals for locally Hamiltonian flows
- Torus counting and self-joinings of Kleinian groups
- Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments
- On the integral Hodge conjecture for real abelian threefolds
- Weakly Kähler hyperbolic manifolds and the Green–Griffiths–Lang conjecture
