The dimension of the Hilbert Space of Geometic quantization of vortices on a Riemann surface

TL;DR

This paper calculates the dimension of the Hilbert space resulting from geometric quantization of vortex moduli spaces on Riemann surfaces, linking it to the holomorphic Euler characteristic of a quantum line bundle.

Contribution

It provides a precise computation of the Hilbert space dimension for vortex moduli spaces using Kähler quantization methods.

Findings

Dimension equals the holomorphic Euler characteristic of the quantum line bundle

Explicit formula for the Hilbert space dimension on Riemann surfaces

Connects geometric quantization with topological invariants

Abstract

In this article we calculate the dimension of the Hilbert space of Kahler quantization of the moduli space of vortices on a Riemann surface. This dimension is given by the holomorphic Euler characteristic of the quantum line bundle.