On Ballico-Hefez curves and associated supersingular surfaces
Algebraic Geometry
2014-02-17 v1
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.
Keywords
Cite
@article{arxiv.1402.3372,
title = {On Ballico-Hefez curves and associated supersingular surfaces},
author = {Hoang Thanh Hoai and Ichiro Shimada},
journal= {arXiv preprint arXiv:1402.3372},
year = {2014}
}
Comments
12pages