On the Kodaira dimension of $\overline{\mathcal{N}}_{g,n}$
Schwarz, Irene
arXiv, 1811.01193 / Harvested from arXiv
We show that the compactification of the moduli space of $n-$nodal curves of genus g, i.e. $\mathcal{N}_{g,n}:= \mathcal{M}_{g,2n} /G$, with $G:=(\mathbb{Z}_2)^n \rtimes S_n$, is of general type for $g \geq 24$, for all $n \in \mathbb{N}$. While this is a fairly easy result, it requires completely different techniques to extend it to low genus $5 \leq g \leq 23$. Here we need that the number of nodes varies in a band $n_{\mathrm{min}}(g) \leq n \leq n_{\mathrm{max}}(g)$, where $n_{\mathrm{max}}(g)$ is the largest integer smaller than (or in some cases equal to) $\frac{7}{2}(g-1)-3$. The lower bound $n_{\mathrm{min}}(g) $ is close to the bound found by Logan and Farkas for $\mathcal{M}_{g,2n}$ to be of general type (in many cases it is identical). This will be tabled in Theorem 1.1 which is the main result of this paper.
Publié le : 2018-11-03
Classification:  Mathematics - Algebraic Geometry
@article{1811.01193,
     author = {Schwarz, Irene},
     title = {On the Kodaira dimension of $\overline{\mathcal{N}}\_{g,n}$},
     journal = {arXiv},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1811.01193}
}
Schwarz, Irene. On the Kodaira dimension of $\overline{\mathcal{N}}_{g,n}$. arXiv, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/1811.01193/