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arXiv · 2403.02770

Inseparable Kummer surfaces

Yuya Matsumoto
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Abstract

We introduce an inseparable version of Kummer surfaces. It is defined as a supersingular K3 surface in characteristic 2 with 16 smooth rational curves forming a certain configuration and satisfying a suitable divisibility condition. The main result is that such a surface admits an inseparable double covering by a non-normal surface $A$ that is similar to abelian surfaces in two aspects: its numerical invariants are the same as abelian surfaces, and its smooth locus admits an abelian group structure.

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Yuya Matsumoto. 2024-03-05. Inseparable Kummer surfaces. https://arxiv.org/abs/2403.02770

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