On the slope of the moduli space of genus 15 and 16 curves

Abstract

We revisit the work of Chang and Ran on bounding the slopes of $\overline{{\mathcal{M}}_{15}}$ and $\overline{{\mathcal{M}}_{16}}$, correct one of the formulas used at the conclusion of the argument, and recompute the lower bounds on the slopes, yielding $s(\overline{{\mathcal{M}}_{15}})>6.5$ but not for $\overline{{\mathcal{M}}_{16}}$. Our contribution only involves plugging in formulas.

3 pages, comments and corrections welcome