Pencils on surfaces with normal crossings and the Kodaira dimension of ${\overline{\mathcal{M}}}_{g,n}$

Abstract

We study smoothing of pencils of curves on surfaces with normal crossings. As a consequence we show that the canonical divisor of ${\overline{\mathcal{M}}}_{g,n}$ is not pseudo-effective in some range, implying that ${\overline{\mathcal{M}}}_{12,6},{\overline{\mathcal{M}}}_{12,7},{\overline{\mathcal{M}}}_{13,4}$ and ${\overline{\mathcal{M}}}_{14,3}$ are uniruled. We provide upper bounds for the Kodaira dimension of ${\overline{\mathcal{M}}}_{12,8}$ and ${\overline{\mathcal{M}}}_{16}$. We also show that the moduli of $(4g+5)$-pointed hyperelliptic curves ${\mathcal{H}}_{g,4g+5}$ is uniruled. Together with a recent result of Schwarz, this concludes the Kodaira classification for moduli of pointed hyperelliptic curves.

23 pages. Published version. Minor corrections after referee report

References in corpus (3)

• The Kodaira dimensions of ${\overline{\mathcal{M}}}_{22}$ and ${\overline{\mathcal{M}}}_{23}$
• On the slope of the moduli space of genus 15 and 16 curves
• On the Kodaira dimension of the moduli space of hyperelliptic curves with marked points

Cited by in corpus (1)

• On the Kodaira dimension of the moduli space of curves of genus 16