The 2-divisibility of divisors on K3 surfaces in characteristic 2
Algebraic Geometry
2024-10-21 v1 Cryptography and Security
Abstract
We show that K3 surfaces in characteristic 2 can admit sets of disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each . 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 is possible.
Cite
@article{arxiv.2410.14085,
title = {The 2-divisibility of divisors on K3 surfaces in characteristic 2},
author = {Toshiyuki Katsura and Shigeyuki Kondō and Matthias Schütt},
journal= {arXiv preprint arXiv:2410.14085},
year = {2024}
}
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28 pages