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The 2‐divisibility of divisors on K3 surfaces in characteristic 2

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  • Toshiyuki Katsura
  • Shigeyuki Kondō
  • Matthias Schütt

Abstract

We show that K3 surfaces in characteristic 2 can admit sets of n$n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each n=8,12,16,20$n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only n=8$n=8$ is possible.

Suggested Citation

  • Toshiyuki Katsura & Shigeyuki Kondō & Matthias Schütt, 2025. "The 2‐divisibility of divisors on K3 surfaces in characteristic 2," Mathematische Nachrichten, Wiley Blackwell, vol. 298(6), pages 1964-1988, June.
    • Handle: RePEc:bla:mathna:v:298:y:2025:i:6:p:1964-1988
    DOI: 10.1002/mana.12024
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