Geometric prequantization of the moduli space of the vortex equations on a Riemann surface (vol 47, 103501, 2006)

摘要

In this erratum to a work done previously, we give an alternative description for the prequantization with respect to the forms Omega(psi 0), where we do not need the 1-form theta which may not be globally defined. Next by modifying the Quillen metric of the usual determinant bundle suitably, we quantize the usual symplectic form Omega on the vortex moduli space. Next, we show that by modifying the Quillen metric, one can also interpolate between the forms Omega and Omega(psi 0) and the corresponding prequantum line bundles are topologically equivalent. It is not clear whether they are holomorphically equivalent.