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We prove the conjectural formula for the $L^2$ volume of the space of degree$r$ holomorphic maps from a compact K\"ahler 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.

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