Biswas, Indranil
(2007)
*A cohomological criterion for semistable parabolic vector bundles on a curve*
Comptes Rendus Mathematique, 345
(6).
pp. 325-328.
ISSN 1631-073X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S16310...

Related URL: http://dx.doi.org/10.1016/j.crma.2007.07.004

## Abstract

Let X be an irreducible smooth complex projective curve and S ⊂ X a finite subset. Fix a positive integer N. We consider all the parabolic vector bundles over X whose parabolic points are contained in S and all the parabolic weights are integral multiples on 1/N. We construct a parabolic vector bundle V, of this type, satisfying the following condition: a parabolic vector bundle E_{x} of this type is parabolic semistable if and only if there is a parabolic vector bundle F_{x}, also of this type, such that the underlying vector bundle (E_{x}⊗ F_{x}⊗ V_{x})_{0} for the parabolic tensor product E_{x}⊗ F_{x}⊗ V_{x})_{0} is cohomologically trivial, which means that H^{i}(X,(E_{x}⊗ F_{x}⊗ V_{x})_{0}) = 0 for all i. Given any parabolic semistable vector bundle E_{x}, the existence of such F_{x} is proved using a criterion of Faltings which says that a vector bundle E over X is semistable if and only if there is another vector bundle F such that E⊗F is cohomologically trivial.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

ID Code: | 3487 |

Deposited On: | 12 Oct 2010 04:30 |

Last Modified: | 12 Oct 2010 04:30 |

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