K3 surfaces with ten cusps
Ichiro Shimada, De-Qi Zhang
TL;DR
This paper proves that normal K3 surfaces with ten cusps exist exclusively in characteristic 3, classifies them by polarization degree, and provides explicit examples.
Contribution
It establishes the existence and uniqueness of such K3 surfaces in characteristic 3 and classifies them based on polarization degree.
Findings
Existence of K3 surfaces with ten cusps only in characteristic 3
Classification according to polarization degrees
Explicit examples of these surfaces provided
Abstract
We show that normal K3 surfaces with ten cusps exist in and only in characteristic 3. We determine these K3 surfaces according to the degrees of the polarizations. Explicit examples are given.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Finite Group Theory Research · Coding theory and cryptography