Smooth subvarieties of Jacobians

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

1 CNRS - Centre National de la Recherche Scientifique
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We give new examples of algebraic integral cohomology classes on smooth projective complex varieties that are not integral linear combinations of classes of smooth subvarieties. Some of our examples have dimension 6, the lowest possible. The classes that we consider are minimal cohomology classes on Jacobians of very general curves. Our main tool is complex cobordism.

Mots clés: Algebraic cycles; Jacobians; complex cobordism

Domaines: Mathématiques [math]

Olivier Benoist, Olivier Debarre. Smooth subvarieties of Jacobians. Épijournal de Géométrie Algébrique, 2023, ⟨10.46298/epiga.2023.10321⟩. ⟨hal-04463495⟩