Let X be a compact Riemann surface and associated to each point p-i of a finite subset S of X is a positive integer m-i. Fix an elliptic curve C. To this data we associate a smooth elliptic surface Z fibered over X. The group C acts on Z with X as the quotient. It is shown that the space of all vector bundles over Z equipped with a lift of the action of C is in bijective correspondence with the space of all parabolic bundles over X with parabolic structure over S and the parabolic weights at any p-i being integral multiples of 1 / m-i. A vector bundle V over Z equipped with an action of C is semistable (respectively, polystable) if and only if the parabolic bundle on X corresponding to V is semistable (respectively, polystable). This bijective correspondence is extended to the context of principal bundles.
@article{urn:eudml:doc:44320,
title = {Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.},
journal = {Collectanea Mathematica},
volume = {54},
year = {2003},
pages = {293-308},
zbl = {1048.14014},
mrnumber = {MR2010791},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44320}
}
Biswas, Indranil. Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.. Collectanea Mathematica, Tome 54 (2003) pp. 293-308. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44320/