Determinants of parabolic bundles on Riemann surfaces (Q1210535)

The authors construct a metrized holomorphic line bundle on the moduli space \(M^ p_ s(X)\) of stable parabolic vector bundles with fixed rank, degree, rational weights and multiplicities over a compact Riemann surface \(X\). To formulate the results the authors first recall basic definitions about parabolic bundles and \(\pi\)-bundles with related notions such as semi-stable and stable parabolic bundles. Next, the authors define and discuss the determinants of \(\pi\)-bundles and then construct the moduli space of stable \(\pi\)-bundles. Finally, the authors prove that there exists on \(M^ p_ s(X)\) a metrized line bundle \(L^ p\) whose Chern form has a nice relation with the natural Kähler form.