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June 2004 On the Moduli Space of Pointed Algebraic Curves of Low Genus ---A Computational Approach---
Tatsuji MORI, Tetsuo NAKANO
Tokyo J. Math. 27(1): 239-253 (June 2004). DOI: 10.3836/tjm/1244208488

Abstract

We compute explicitly the moduli space $\mathcal{M}_{g,1}^N$ of pointed algebraic curves of genus $g$ with a given numerical semigroup $N$ when $g$ is small ($2 \leq g \leq 5$). It is known that such a moduli space $\mathcal{M}_{g,1}^N$ is non-empty for $g \leq 7$. The main results obtained in this note are the irreducibility and the determination of the dimension of $\mathcal{M}_{g,1}^N$ for $g \leq 5$ except a few cases. In particular, it turns out that many of these moduli spaces are unirational.

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Tatsuji MORI. Tetsuo NAKANO. "On the Moduli Space of Pointed Algebraic Curves of Low Genus ---A Computational Approach---." Tokyo J. Math. 27 (1) 239 - 253, June 2004. https://doi.org/10.3836/tjm/1244208488

Information

Published: June 2004
First available in Project Euclid: 5 June 2009

zbMATH: 1077.14037
MathSciNet: MR2060088
Digital Object Identifier: 10.3836/tjm/1244208488

Rights: Copyright © 2004 Publication Committee for the Tokyo Journal of Mathematics

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Vol.27 • No. 1 • June 2004
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