Geometric Prequantization of the Seiberg-Witten Moduli Space on Product of a Riemann Surface

Abstract

We show the existence of a symplectic structure on the moduli space of he Seiberg-Witten equations on $\Sigma\times\Sigma$ where $\Sigma$ is a compact Riemann surface. To prequantize the moduli space, we construct a Quillen-type determinant line bundle on it and show its curvature is proportional to the symplectic form.