English

Parabolic bundles and representations of the fundamental group

Algebraic Geometry 2007-05-23 v1

Abstract

Let X be as smooth complex projective variety with Neron-Severi group isomorphic to Z, and D an irreducible divisor with normal crossing singularities. Assume r is equal to 2 or 3. We prove that if the fundamental group of X doesn't have irreducible PU(r) representations, then the fundamental group of X-D doesn't have irreducible U(r) representations. The proof uses the non-existence of certain stable parabolic bundles. We also obtain a similar result for GL(2) when D is smooth and X is a complex surface.

Keywords

Cite

@article{arxiv.math/9912003,
  title  = {Parabolic bundles and representations of the fundamental group},
  author = {Tomas L. Gomez and T. R. Ramadas},
  journal= {arXiv preprint arXiv:math/9912003},
  year   = {2007}
}

Comments

13 pages, 1 figure, LaTeX2e