On the integral Hodge conjecture for real varieties, I

Olivier Benoist (1, 2) , Olivier Wittenberg (1, 3)

1 CNRS - Centre National de la Recherche Scientifique
2 IRMA - Institut de Recherche Mathématique Avancée
3 DMA - Département de Mathématiques et Applications - ENS Paris

We formulate the "real integral Hodge conjecture", a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi-Yau threefolds and on rationally connected varieties. We relate it to the problem of determining the image of the Borel-Haefliger cycle class map for 1-cycles, with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the Chow group of 1-cycles of real threefolds. New results about these problems are obtained along the way.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Olivier Benoist, Olivier Wittenberg. On the integral Hodge conjecture for real varieties, I. Inventiones Mathematicae, 2020, 222, pp.1-77. ⟨10.1007/s00222-020-00965-8⟩. ⟨hal-02358003⟩