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

Chih-Chung Liu

arxiv: 1504.01021 · v2 · pith:62DH3UMYnew · submitted 2015-04-04 · 🧮 math-ph · math.MP

The L² Volume of the Space of Holomorphic Maps from K\"ahler Riemann Surfaces to mathbb{CP}^k

Chih-Chung Liu This is my paper

classification 🧮 math-ph math.MP

keywords ahlerciteformulaholomorphicmapsriemannspacevolume

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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.

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The L² Volume of the Space of Holomorphic Maps from K\"ahler Riemann Surfaces to mathbb{CP}^k

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