English

Torsion orders of Fano hypersurfaces

Algebraic Geometry 2021-03-03 v2 Number Theory

Abstract

We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields of arbitrary characteristic. Our results imply that unirational parametrizations of most Fano hypersurfaces need to have enormously large degree. Our results also hold in characteristic two, where they solve the rationality problem for hypersurfaces under a logarithmic degree bound, thereby extending a previous result of the author from characteristic different from two to arbitrary characteristic.

Keywords

Cite

@article{arxiv.1911.12271,
  title  = {Torsion orders of Fano hypersurfaces},
  author = {Stefan Schreieder},
  journal= {arXiv preprint arXiv:1911.12271},
  year   = {2021}
}

Comments

32 pages, final version, to appear in Algebra and Number Theory