The $L^2$ Volume of the Space of Holomorphic Maps from Kähler Riemann Surfaces to $\mathbb{CP}^k$

Abstract

We prove the conjectural formula for the $L^2$ volume of the space of degree $r$ holomorphic maps from a compact Kähler Riemann surface of genus $b$ to $\pk$. This formula was posed in \cite{Ba} and rigorously verified in \cite{Sp} for a special case using independent techniques.