The line bundles on the stack of parabolic $G$-bundles over curves and their sections

Details The line bundles on the stack of parabolic $G$-bundles over curves and their sections The line bundles on the stack of parabolic $G$-bundles over curves and their sections

1995-07-05

arxiv.org/abs/alg-geom/9507002v3

Mathematics

Algebraic Geometry

LaTeX2e with package amsart, 31 pages, no figures. This is a revised version of our paper (mainly, the introduction and the se

Scientific paper

Let $X$ be a smooth, complete and connected curve and $G$ be a simple and simply connected algebraic group over $\comp$. We calculate the Picard group of the moduli stack of quasi-parabolic $G$-bundles and identify the spaces of sections of its members to the conformal blocs of Tsuchiya, Ueno and Yamada. We describe the canonical sheaf on these stacks and show that they admit a unique square root, which we will construct explicitly. Finally we show how the results on the stacks apply to the coarse moduli spaces and recover (and extend) the Drezet-Narasimhan theorem. We show moreover that the coarse moduli spaces of semi-stable $SO_r$-bundles are not locally factorial for $r\geq 7$.

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