Let $f$ be a meromorphic function on a compact Riemann surface $X$ and let $m$ be the standard round
metric of curvature $1$ on the Riemann sphere. Then the pullback $f^*m$ of $m$ under $f$ is a metric on
$X$ of curvature $1$ with conical singularities at the critical points of $f$. We study the $\zeta$-regularized
determinant of the Laplace operator on $X$ corresponding to the metric $f^*m$ as a functional on the moduli
space of pairs $(X, f)$ and derive an explicit formula for the functional. The talk is based on the joint work
with V. Kalvin (Concordia University).
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5312