Metrics of constant positive curvature with conical singularities, Hurwitz spaces, and $\det \Delta$

Victor Kalvin, Alexey Kokotov

Let $f:X\to \mathbb{C}{P}^1$ be a meromorphic function of degree $N$ with simple poles and simple critical points on a compact Riemann surface $X$ of genus $g$ and let $\mathsf{m}$ be…