On deformations of quintic and septic hypersurfaces

Research output: Contribution to journal › Article › Research › peer review

Authors

  • John Christian Ottem
  • Stefan Schreieder

External Research Organisations

  • University of Oslo
  • Ludwig-Maximilians-Universität München (LMU)
View graph of relations

Details

Original languageEnglish
Pages (from-to)140-158
Number of pages19
JournalJournal des Mathematiques Pures et Appliquees
Volume135
Publication statusPublished - 6 Dec 2019
Externally publishedYes

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

    Deformation, Hypersurface, Moduli, Quintic, Septic

ASJC Scopus subject areas

Cite this

On deformations of quintic and septic hypersurfaces. / Ottem, John Christian; Schreieder, Stefan.
In: Journal des Mathematiques Pures et Appliquees, Vol. 135, 06.12.2019, p. 140-158.

Research output: Contribution to journal › Article › Research › peer review

Ottem JC, Schreieder S. On deformations of quintic and septic hypersurfaces. Journal des Mathematiques Pures et Appliquees. 2019 Dec 6;135:140-158. doi: 10.1016/j.matpur.2019.12.013
Ottem, John Christian ; Schreieder, Stefan. / On deformations of quintic and septic hypersurfaces. In: Journal des Mathematiques Pures et Appliquees. 2019 ; Vol. 135. pp. 140-158.
Download
@article{49e1f131e8154f2b979d0658b58bb197,
title = "On deformations of quintic and septic hypersurfaces",
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 = "Deformation, Hypersurface, Moduli, Quintic, Septic",
author = "Ottem, {John Christian} and Stefan Schreieder",
note = "Funding information: Supported by the Research Council of Norway (project no. 250104).",
year = "2019",
month = dec,
day = "6",
doi = "10.1016/j.matpur.2019.12.013",
language = "English",
volume = "135",
pages = "140--158",
journal = "Journal des Mathematiques Pures et Appliquees",
issn = "0021-7824",
publisher = "Elsevier Masson SAS",

}

Download

TY - JOUR

T1 - On deformations of quintic and septic hypersurfaces

AU - Ottem, John Christian

AU - Schreieder, Stefan

N1 - Funding information: Supported by the Research Council of Norway (project no. 250104).

PY - 2019/12/6

Y1 - 2019/12/6

N2 - 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.

AB - 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.

KW - Deformation

KW - Hypersurface

KW - Moduli

KW - Quintic

KW - Septic

UR - http://www.scopus.com/inward/record.url?scp=85076854854&partnerID=8YFLogxK

U2 - 10.1016/j.matpur.2019.12.013

DO - 10.1016/j.matpur.2019.12.013

M3 - Article

AN - SCOPUS:85076854854

VL - 135

SP - 140

EP - 158

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

SN - 0021-7824

ER -