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