On deformations of quintic and septic hypersurfaces

verfasst von

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.

Externe Organisation(en)

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

Typ

Artikel

Journal

Journal des Mathematiques Pures et Appliquees

Band

135

Seiten

140-158

Anzahl der Seiten

19

ISSN

0021-7824

Publikationsdatum

06.12.2019

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.), Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.1016/j.matpur.2019.12.013 (Zugang: Geschlossen)
https://arxiv.org/abs/1810.12711 (Zugang: Offen)