Mathematische Annalen

, Volume 368, Issue 1–2, pp 753–809

Lines on quartic surfaces

  • Alex Degtyarev
  • Ilia Itenberg
  • Ali Sinan Sertöz
Article

DOI: 10.1007/s00208-016-1484-0

Cite this article as:
Degtyarev, A., Itenberg, I. & Sertöz, A.S. Math. Ann. (2017) 368: 753. doi:10.1007/s00208-016-1484-0

Abstract

We show that the maximal number of (real) lines in a (real) nonsingular spatial quartic surface is 64 (respectively, 56). We also give a complete projective classification of all quartics containing more than 52 lines: all such quartics are projectively rigid. Any value not exceeding 52 can appear as the number of lines of an appropriate quartic.

Mathematics Subject Classification

Primary 14J28 Secondary 14J27 14N25 

Funding information

Funder NameGrant NumberFunding Note
TÜBİTAK
  • 114F325
  • 114F325
FRG
  • DMS-1265228
JSPS
  • L15517

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Alex Degtyarev
    • 1
  • Ilia Itenberg
    • 2
    • 3
  • Ali Sinan Sertöz
    • 1
  1. 1.Department of MathematicsBilkent UniversityAnkaraTurkey
  2. 2.Institut de Mathématiques de Jussieu–Paris Rive GaucheUniversité Pierre et Marie CurieParis Cedex 5France
  3. 3.Département de Mathématiques et ApplicationsEcole Normale SupérieureParis Cedex 5France

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