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The Kodaira dimensions of $\overline{\mathcal{M}}_{22}$ and $\overline{\mathcal{M}}_{23}$
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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.
Forward citations
Cited by 3 Pith papers
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The Kodaira classification of the moduli space of pointed curves in genus $3$
For n≥15, the moduli space of n-pointed genus-3 curves is of general type, completing the Kodaira classification of pointed genus-3 moduli spaces.
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Tropical linear systems and the realizability problem
Local dimension of a tropical linear system is bounded below by its Baker-Norine rank, and the realizable canonical divisors form a tropically convex, definable, closed polyhedral complex.
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Tropical geometry in torus bundles
For curves in a torus bundle, the weighted sum of tropical edge directions equals the Chern classes of the bundle line bundles evaluated on the curve's base class.
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