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

Toshiyuki Katsura, Shigeyuki Kondō and Matthias Schütt

Mathematische Nachrichten, 2025, vol. 298, issue 6, 1964-1988

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.

Date: 2025
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