Curvature of the determinant bundle and the Kähler form over the moduli of parabolic bundles for a family of pointed curves (Q1275242)

Let \(f: X_T\to T\) be a holomorphic family of Riemann surfaces and fix disjoint sections \(s_1,\dots, s_n\) of \(f\). We have a family of Riemann surfaces with \(n\) marked points parametrized by \(T\). Let \(F: M^P_T\to T\) be the relative moduli space of parabolic stable vector bundles of rank \(r\) and parabolic degree zero with given parabolic data at the marked points. Generalizing a result of one of the authors [Ann. Inst. Fourier 47, 885-913 (1997; Zbl 0873.32017)], the authors define the parabolic determinant line bundle over \(M^P_T\), construct a natural Hermitian metric on this determinant bundle, and compute the curvature of the corresponding Hermitian connection.