On deformations of quintic and septic hypersurfaces
Algebraic Geometry
2020-11-30 v2 Complex Variables
Abstract
An old question of Mori asks whether in dimension at least three, any smooth specialization of a hypersurface of prime degree is again a hypersurface. A positive answer to this question is only known in degrees two and three. In this paper, we settle the case of quintic hypersurfaces (in arbitrary dimension) as well as the case of septics in dimension three. Our results follow from numerical characterizations of the corresponding hypersurfaces. In the case of quintics, this extends famous work of Horikawa who analysed deformations of quintic surfaces.
Keywords
Cite
@article{arxiv.1810.12711,
title = {On deformations of quintic and septic hypersurfaces},
author = {John Christian Ottem and Stefan Schreieder},
journal= {arXiv preprint arXiv:1810.12711},
year = {2020}
}
Comments
23 pages, final version, to appear in Journal de Math\'ematiques Pures et Appliqu\'ees