Mathematics – Algebraic Geometry
Scientific paper
2012-04-19
Mathematics
Algebraic Geometry
8 pages. to appear in: Central European Journal of Mathematics
Scientific paper
Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let M_{r,L}^{ss} denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant L. We prove Pic(M_{r,L}^{ss}) = Z, identify the ample generator, and deduce that M_{r,L}^{ss} is locally factorial. In characteristic zero, this has already been proved by Dr\'{e}zet and Narasimhan. The main point of the present note is to circumvent the usual problems with Geometric Invariant Theory in positive caracteristic.
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