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December 2016 On the Moduli Space of Pointed Algebraic Curves of Low Genus III ---Positive Characteristic---
Tetsuo NAKANO
Tokyo J. Math. 39(2): 565-582 (December 2016). DOI: 10.3836/tjm/1484903137

Abstract

In his classical work, Pinkham discovered a beautiful theorem on the moduli space of pointed algebraic curves with a fixed Weierstrass gap sequence at the marked point. Namely, the complement of a Weierstrass gap sequence in the set of non-negative integers is a numerical semigroup, and he described such a moduli space in terms of the negative part of the miniversal deformation space of the monomial curve of this semigroup. Unfortunately, his theorem holds only in characteristic 0 and does not hold in positive characteristic in general. In this paper, we will study his theorem in positive characteristic, and give a fairly sharp condition for his theorem to hold in positive characteristic up to genus 4. As an application, we present a complete analysis of his theorem in positive characteristic in the low genus case.

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Tetsuo NAKANO. "On the Moduli Space of Pointed Algebraic Curves of Low Genus III ---Positive Characteristic---." Tokyo J. Math. 39 (2) 565 - 582, December 2016. https://doi.org/10.3836/tjm/1484903137

Information

Published: December 2016
First available in Project Euclid: 20 January 2017

zbMATH: 1370.14030
MathSciNet: MR3599509
Digital Object Identifier: 10.3836/tjm/1484903137

Subjects:
Primary: 14H10
Secondary: 14H55

Rights: Copyright © 2016 Publication Committee for the Tokyo Journal of Mathematics

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Vol.39 • No. 2 • December 2016
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