Determinants of parabolic bundles on Riemann surfaces

Abstract

Let X be a compact Riemann surface and M_s^p(X) the moduli space of stable parabolic vector bundles with fixed rank, degree, rational weights and multiplicities. There is a natural Kahler metric on M_s^p(X). We obtain a natural metrized holomorphic line bundle on M_s^p(X) whose Chern form equals mr times the Kahler form, where m is the common denominator of the weights and r the rank.