MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

In the original paper of Mehta-Seshadri, it seems like they treat the case of zero parabolic degree (i.e. they prove that zero parabolic degree stable parabolic bundles correspond to irreps of the fundamental group of the Riemann surface minus some points). But, as in the Narasimhan-Seshadri theorem, is the nonzero degree case obtained by considering representations of a central extension of the fundamental group? I'd be grateful if someone may point to a reference.

share|cite|improve this question
Vamsi, it is hard to understand your question... Maybe you are asking the following: ? Let $V$ be a stable bundle on a curve $C$, and suppose that the degree of $V$ is non-zero. Is it true that one can naturally associate a representation of a central extension of $\pi_1(C)$ to $V$? – Dmitri May 10 '11 at 22:15
If I remember correctly you should find something about that in the volume n.96 of asterisque, "Fibres Vectoriels sur les courbes Algebriques", by Seshadri. – Mattia Talpo May 10 '11 at 22:48
@Dmitri, I mean : Let $V$ be a stable bundle on a smooth curve $C$ and suppose the parabolic degree (=deg(E) + sum of weights of the flags) is not zero. Then, is it true that one can naturally associate a representation of the central extension of $\pi_1$ of $C$ minus some points to $V$? – Vamsi May 10 '11 at 23:12
@Mattia: Thanks. Do you happen to have an online copy of the paper? I can't seem to find it at all? – Vamsi May 10 '11 at 23:14
It turns out I didn't remember correctly, sorry: I just checked and only the degree 0 case is treated. Anyway I don't think an online copy exists, at least I couldn't find one when I was looking for it. – Mattia Talpo May 11 '11 at 9:58
up vote 3 down vote accepted

I think what you want probably follows from Theoreme 2.5 of the paper: Biquard, Olivier: Fibrés paraboliques stables et connexions singulières plates, Bull. Soc. Math. France 119 (1991), no. 2, 231–257.

share|cite|improve this answer
Yeah, thanks. I realised that yesterday (Biquard gives us a projective representation of the fundamental group which then is a representation of an extension of the same). – Vamsi May 13 '11 at 15:46

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.