On deformations of quintic and septic hypersurfaces

authored by

John Christian Ottem, Stefan Schreieder

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.

External Organisation(s)

University of Oslo
Ludwig-Maximilians-Universität München (LMU)

Type

Article

Journal

Journal des Mathematiques Pures et Appliquees

Volume

135

Pages

140-158

No. of pages

19

ISSN

0021-7824

Publication date

06.12.2019

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics(all), Applied Mathematics

Electronic version(s)

https://doi.org/10.1016/j.matpur.2019.12.013 (Access: Closed)
https://arxiv.org/abs/1810.12711 (Access: Open)