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

• Autores: Indranil Biswas
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 54, Fasc. 3, 2003, págs. 293-308
• Idioma: inglés
• Títulos paralelos:
  • Haces principales de tipo orbifold sobre un fibrado elíptico y haces principales parabólicos sobre una superficie de Riemann
• Enlaces
  • Texto completo
• Resumen

  • 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.