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arXiv · 2110.04813

Arithmetic inflection of superelliptic curves

Ethan Cotterill·Ignacio Darago·Cristhian Garay López·Changho Han·Tony Shaska
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Abstract

In this paper, we explore the inflectionary behavior of linear series on superelliptic curves $X$ over fields of arbitrary characteristic. Here we give a precise description of the inflection of linear series over the ramification locus of the superelliptic projection; and we initiate a study of those inflectionary varieties that parameterize the inflection points of linear series on $X$ supported away from the superelliptic ramification locus that is predicated on the behavior of their Newton polytopes.

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Ethan Cotterill, Ignacio Darago, Cristhian Garay López, Changho Han, Tony Shaska. 2021-10-10. Arithmetic inflection of superelliptic curves. https://doi.org/10.1307/mmj/20216152

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