A note on the supersingular K3 surface of Artin invariant 1
Matthias Schuett
TL;DR
This paper proves that the supersingular K3 surface with Artin invariant 1 in characteristic p can be modeled over the finite field with p elements, having a Picard number of 21, enhancing understanding of its algebraic structure.
Contribution
It establishes the existence of a model over IF_p for the supersingular K3 surface of Artin invariant 1 with maximal Picard number, which was previously unknown.
Findings
Existence of a model over IF_p for the surface.
Picard number of the model is 21.
Applicable for any prime p.
Abstract
We prove that the supersingular K3 surface of Artin invariant 1 in characteristic p (where p denotes an arbitrary prime) admits a model over IF_p with Picard number 21.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry