English

Fano varieties with torsion in the third cohomology group

Algebraic Geometry 2023-11-17 v2 Algebraic Topology

Abstract

We construct first examples of Fano varieties with torsion in their third cohomology group. The examples are constructed as double covers of linear sections of rank loci of symmetric matrices, and can be seen as higher-dimensional analogues of the Artin--Mumford threefold. As an application, we answer a question of Voisin on the coniveau and strong coniveau filtrations of rationally connected varieties.

Keywords

Cite

@article{arxiv.2309.10793,
  title  = {Fano varieties with torsion in the third cohomology group},
  author = {John Christian Ottem and Jørgen Vold Rennemo},
  journal= {arXiv preprint arXiv:2309.10793},
  year   = {2023}
}

Comments

24 pages. With an appendix by J\'anos Koll\'ar