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arXiv · 1403.2317

Brill-Noether theory of curves on toric surfaces

Geoffrey Degener Smith
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Abstract

A Laurent polynomial $f$ in two variables naturally describes a projective curve $C(f)$ on a toric surface. We show that if $C(f)$ is a smooth curve of genus at least 7, then $C(f)$ is not Brill-Noether general. To accomplish this, we classify all Newton polygons that admit such curves whose divisors all have nonnegative Brill-Noether number.

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Geoffrey Degener Smith. 2014-03-10. Brill-Noether theory of curves on toric surfaces. https://arxiv.org/abs/1403.2317

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