Arithmetic inflection of superelliptic curves
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866910029331824640 |
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| author | Cotterill, Ethan Darago, Ignacio López, Cristhian Garay Han, Changho Shaska, Tony |
| author_facet | Cotterill, Ethan Darago, Ignacio López, Cristhian Garay Han, Changho Shaska, Tony |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_04813 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Arithmetic inflection of superelliptic curves Cotterill, Ethan Darago, Ignacio López, Cristhian Garay Han, Changho Shaska, Tony Algebraic Geometry Combinatorics Number Theory 14Hxx, 14Mxx, 11Gxx, 05Exx 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. |
| title | Arithmetic inflection of superelliptic curves |
| topic | Algebraic Geometry Combinatorics Number Theory 14Hxx, 14Mxx, 11Gxx, 05Exx |
| url | https://arxiv.org/abs/2110.04813 |