Geometric prequantization of the Seiberg-Witten moduli space on the product of a Riemann surface (Q6045378)

This article constructs (c.f. Theorem 5) a geometric prequantization of the space of Seiberg-Witten equations on the product of a Riemann surface \(\Sigma\times \Sigma\) (see section 2 for the definition of this moduli space), which is shown to be symplectic (c.f. Propositions 3 and 4 in section 3). The line bundle needed for the geometric prequantization (together with an Hermitian netric and a connection whose curvature is proportional to the symplectic form) is a Quillen-type bundle constructed in section 3.