Birationally rigid singular double quadrics and double cubics
Algebraic Geometry
2018-01-30 v2
Abstract
In this paper a large class of Fano double quadrics and cubics are shown to be factorial and birationally superrigid, in particular they admit no non-trivial structure of a fibration with rationally connected fibres and are therefore non-rational. This is shown using the "Method of maximal singularities" of Iskovskikh and Manin, expanded upon by Pukhlikov. In addition, an estimate of the codimension of the set of such varieties is calculated.
Keywords
Cite
@article{arxiv.1604.02560,
title = {Birationally rigid singular double quadrics and double cubics},
author = {Ewan Johnstone},
journal= {arXiv preprint arXiv:1604.02560},
year = {2018}
}
Comments
Second version. The assumptions on dimension and rank of the singularities have been altered slightly. A small regularity condition has been added to the case of double cubics