Lines on K3 quartic surfaces in characteristic 3

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

Authors

  • Davide Cesare Veniani

Research Organisations

External Research Organisations

  • University of Stuttgart
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Details

Original languageEnglish
Pages (from-to)675-701
Number of pages27
JournalManuscripta Mathematica
Volume167
Issue number3-4
Early online date7 Feb 2021
Publication statusPublished - Mar 2022

Abstract

We investigate the number of straight lines contained in a K3 quartic surface X defined over an algebraically closed field of characteristic 3. We prove that if X contains 112 lines, then X is projectively equivalent to the Fermat quartic surface; otherwise, X contains at most 67 lines. We improve this bound to 58 if X contains a star (ie four distinct lines intersecting at a smooth point of X). Explicit equations of three 1-dimensional families of smooth quartic surfaces with 58 lines, and of a quartic surface with 8 singular points and 48 lines are provided.

Cite this

Lines on K3 quartic surfaces in characteristic 3. / Veniani, Davide Cesare.
In: Manuscripta Mathematica, Vol. 167, No. 3-4, 03.2022, p. 675-701.

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

Veniani DC. Lines on K3 quartic surfaces in characteristic 3. Manuscripta Mathematica. 2022 Mar;167(3-4):675-701. Epub 2021 Feb 7. doi: 10.1007/s00229-021-01284-9
Veniani, Davide Cesare. / Lines on K3 quartic surfaces in characteristic 3. In: Manuscripta Mathematica. 2022 ; Vol. 167, No. 3-4. pp. 675-701.
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