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arXiv · 1204.4418

The Picard group of a coarse moduli space of vector bundles in positive characteristic

Norbert Hoffmann
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Abstract

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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Norbert Hoffmann. 2012-04-19. The Picard group of a coarse moduli space of vector bundles in positive characteristic. https://arxiv.org/abs/1204.4418

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