K3 surfaces with 9 cusps in characteristic p
نویسندگان
چکیده
We study K3 surfaces with 9 cusps, i.e. disjoint A 2 configurations of smooth rational curves, over algebraically closed fields characteristic p ? 3 . Much like in the complex situation studied by Barth, we prove that each such surface admits a triple covering an abelian surface. Conversely, determine which order three automorphisms give rise to surfaces. also investigate how cusps hit supersingular locus.
منابع مشابه
K3 Surfaces with Nine Cusps
By a K3-surface with nine cusps I mean a surface with nine isolated double points A 2 , but otherwise smooth, such that its minimal desingularisation is a K3-surface. It is shown, that such a surface admits a cyclic triple cover branched precisely over the cusps. This parallels the theorem of Nikulin, that a K3-surface with 16 nodes is a Kummer quotient of a complex torus.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2021
ISSN: ['1873-1376', '0022-4049']
DOI: https://doi.org/10.1016/j.jpaa.2020.106558