The Kodaira dimensions of $\overline{\mathcal{M}}_{22}$ and $\overline{\mathcal{M}}_{23}$
Algebraic Geometry
2025-03-11 v3
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.
Keywords
Cite
@article{arxiv.2005.00622,
title = {The Kodaira dimensions of $\overline{\mathcal{M}}_{22}$ and $\overline{\mathcal{M}}_{23}$},
author = {Gavril Farkas and David Jensen and Sam Payne},
journal= {arXiv preprint arXiv:2005.00622},
year = {2025}
}
Comments
v3: 109 pages. Minor revisions. To appear in Cambridge J. Math