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arXiv · 2002.10691

Singularities of the dual curve of a certain plane curve in positive characteristic

Kosuke Komeda
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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. 2020-02-25. Singularities of the dual curve of a certain plane curve in positive characteristic. https://arxiv.org/abs/2002.10691

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