The Kodaira dimensions of ${\overline{\mathcal{M}}}_{22}$ and ${\overline{\mathcal{M}}}_{23}$

Abstract

We prove that the moduli spaces of curves of genus 22 and 23 are of general type. To do this, we calculate certain virtual divisor classes of small slope associated to linear series of rank 6 with quadric relations. We then develop new tropical methods for studying linear series and independence of quadrics and show that these virtual classes are represented by effective divisors.

arXiv commentv3: 109 pages. Minor revisions. To appear in Cambridge J. Math

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• The non-abelian Brill-Noether divisor on ${\overline{\mathcal{M}}}_{13}$ and the Kodaira dimension of ${\overline{\mathcal{R}}}_{13}$
• Pencils on surfaces with normal crossings and the Kodaira dimension of ${\overline{\mathcal{M}}}_{g,n}$
• On the Kodaira dimension of the moduli space of curves of genus 16
• Voronoi tilings, toric arrangements and degenerations of line bundles III
• Poincaré Series of Divisors on Graphs and Chains of Loops