Kodai Mathematical Journal

On Ballico-Hefez curves and associated supersingular surfaces

Thanh Hoai Hoang and Ichiro Shimada

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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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Kodai Math. J., Volume 38, Number 1 (2015), 23-36.

First available in Project Euclid: 18 March 2015

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Hoang, Thanh Hoai; Shimada, Ichiro. On Ballico-Hefez curves and associated supersingular surfaces. Kodai Math. J. 38 (2015), no. 1, 23--36. doi:10.2996/kmj/1426684441. https://projecteuclid.org/euclid.kmj/1426684441

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