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

Collectanea Mathematica (2003)

- Volume: 54, Issue: 3, page 293-308
- ISSN: 0010-0757

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topBiswas, 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 -

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