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March 2021 Singularities of the dual curve of a certain plane curve in positive characteristic
Kosuke Komeda
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Kodai Math. J. 44(1): 166-180 (March 2021). DOI: 10.2996/kmj44110

Abstract

It is well known that the Gauss map for a complex plane curve is birational, whereas the Gauss map in positive characteristic is not always birational. Let $q$ be a power of a prime integer. We study a certain plane curve of degree $q^2 + q + 1$ for which the Gauss map is inseparable with inseparable degree $q$. As a special case, we show a relation between the dual curve of the Fermat curve of degree $q^2 + q + 1$ and the Ballico-Hefez curve.

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Kosuke Komeda. "Singularities of the dual curve of a certain plane curve in positive characteristic." Kodai Math. J. 44 (1) 166 - 180, March 2021. https://doi.org/10.2996/kmj44110

Information

Received: 17 February 2020; Revised: 17 September 2020; Published: March 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.2996/kmj44110

Subjects:
Primary: 14H50
Secondary: 14H20

Keywords: dual curve , plane curve , positive characteristic , singularity

Rights: Copyright © 2021 Tokyo Institute of Technology, Department of Mathematics

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Vol.44 • No. 1 • March 2021
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