On deformations of quintic and septic hypersurfaces

Ottem, John Christian und Schreieder, Stefan (2020): On deformations of quintic and septic hypersurfaces. In: Journal De Mathematiques Pures et Appliquees, Bd. 135: S. 140-158

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. (C) 2019 Elsevier Masson SAS. All rights reserved.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0021-7824
• Sprache: Englisch