Quillen-type bundle and geometric prequantization on moduli space of the Seiberg-Witten equations on product of Riemann surfaces

Abstract

We show the existence of a symplectic structure on the moduli space of the Seiberg-Witten equations on $\Sigma \times \Sigma$ where $\Sigma$ is a compact oriented 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.