arXiv research

Compactifies strata of d-differentials in genus 0.

Given $d\in \mathbb{N}$, $g\in \mathbb{N} \cup\{0\}$, and an integral vector $κ=(k_1,\dots,k_n)$ such that $k_i>-d$ and $k_1+\dots+k_n=d(2g-2)$, let $Ω^d\mathcal{M}_{g,n}(κ)$ denote the moduli space of meromorphic $d$-differentials on Riemann surfaces of genus $g$ whose zeros and poles have orders prescribed by $κ$. We…

Generalized meshes for non-regular geometries, including fractures.

The paper calculates volumes of moduli spaces of flat metrics on spheres with specific angles.