On Ballico-Hefez curves and associated supersingular surfaces

Hoang Thanh Hoai; Ichiro Shimada

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arXiv · 1402.3372

On Ballico-Hefez curves and associated supersingular surfaces

Hoang Thanh Hoai·Ichiro Shimada

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Abstract

Let p be a prime integer, and q a power of p. The Ballico-Hefez curve is a non-reflexive nodal rational plane curve of degree q+1 in characteristic p. We investigate its automorphism group and defining equation. We also prove that the surface obtained as the cyclic cover of the projective plane branched along the Ballico-Hefez curve is unirational, and hence is supersingular. As an application, we obtain a new projective model of the supersingular K3 surface with Artin invariant 1 in characteristic 3 and 5.

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BibTeX RIS

Hoang Thanh Hoai, Ichiro Shimada. 2014-02-14. On Ballico-Hefez curves and associated supersingular surfaces. https://arxiv.org/abs/1402.3372

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