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Determinants of parabolic bundles on Riemann surfaces. (English) Zbl 0779.32021
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.

32G08 Deformations of fiber bundles
32G13 Complex-analytic moduli problems
53B35 Local differential geometry of Hermitian and Kählerian structures
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