Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.

Biswas, Indranil. "Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.." Collectanea Mathematica 54.3 (2003): 293-308. <http://eudml.org/doc/44320>.

@article{Biswas2003,
abstract = {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.},
author = {Biswas, Indranil},
journal = {Collectanea Mathematica},
keywords = {Espacios y haces de fibras; Fibrados; Fibraciones principales; Superficies Riemann},
language = {eng},
number = {3},
pages = {293-308},
title = {Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.},
url = {http://eudml.org/doc/44320},
volume = {54},
year = {2003},
}

TY - JOUR
AU - Biswas, Indranil
TI - Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.
JO - Collectanea Mathematica
PY - 2003
VL - 54
IS - 3
SP - 293
EP - 308
AB - 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.
LA - eng
KW - Espacios y haces de fibras; Fibrados; Fibraciones principales; Superficies Riemann
UR - http://eudml.org/doc/44320
ER -