Mathematische Annalen

, Volume 368, Issue 1–2, pp 753–809 | Cite as

Lines on quartic surfaces

  • Alex Degtyarev
  • Ilia Itenberg
  • Ali Sinan Sertöz
Article

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 

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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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