Parabolic bundles and representations of the fundamental group

Tomas L. Gomez; T. R. Ramadas

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arXiv · math/9912003

Parabolic bundles and representations of the fundamental group

Tomas L. Gomez·T. R. Ramadas

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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.

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BibTeX RIS

Tomas L. Gomez, T. R. Ramadas. 1999-12-01. Parabolic bundles and representations of the fundamental group. https://arxiv.org/abs/math/9912003

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