On BallicoHefez curves and associated supersingular surfaces
Abstract
Let p be a prime integer, and q a power of p. The BallicoHefez curve is a nonreflexive 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 BallicoHefez 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.3372
 Bibcode:
 2014arXiv1402.3372T
 Keywords:

 Mathematics  Algebraic Geometry;
 14H45;
 14J25;
 14J28
 EPrint:
 12pages