# Equivalence between parabolic bundles and bundles on orbicurves

"Everyone knows" that there is an equivalence between vector bundles on a smooth complete orbicurve and parabolic bundles with rational weights on its coarse moduli space. Roughly, it proceeds by pulling back the bundle, then performing elementary modifications along the flags.

But is this thoroughly explained anywhere in the literature? I know the paper of Furuta-Steer, but that is really about a Mehta-Seshadri-type result in differential geometry, associating flat connections with poles to both, whereas I seek a purely algebraic statement.

Also, is anything similar true for principal bundles with reductive structure group? Why?

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There is a paper of Niels Borne, "Sur les représentations du groupe fondamental d'une variété privée d'un diviseur à croisements normaux simples", http://arxiv.org/abs/0704.1236, in which this is carefully written and generalized to any smooth variety with a divisor with simple normal crossing.

I don't know about principal bundles.

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Thanks Angelo & greetings from Vancouver! –  Michael Thaddeus Aug 13 '11 at 7:39
To Michael: enjoy you stay; I'd like to be there too. –  Angelo Aug 13 '11 at 7:42