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.
Citation
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
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