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arXiv · 1207.1239

Genus 1 fibrations on the supersingular K3 surface in characteristic 2 with Artin invariant 1

Noam D. Elkies·Matthias Schuett
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Abstract

The supersingular K3 surface X in characteristic 2 with Artin invariant 1 admits several genus 1 fibrations (elliptic and quasi-elliptic). We use a bijection between fibrations and definite even lattices of rank 20 and discriminant 4 to classify the fibrations, and exhibit isomorphisms between the resulting models of X. We also study a configuration of (-2)-curves on X related to the incidence graph of points and lines of IP^2(IF_4).

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Noam D. Elkies, Matthias Schuett. 2014-03-28. Genus 1 fibrations on the supersingular K3 surface in characteristic 2 with Artin invariant 1. https://arxiv.org/abs/1207.1239

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