Low dimensional projective groups

Indranil Biswas; Mahan Mj

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arXiv · 1203.4520

Low dimensional projective groups

Indranil Biswas·Mahan Mj

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Abstract

We initiate the study of holomorphically convex groups: groups that can be realized as fundamental groups of smooth complex projective varieties with holomorphically convex universal covers. If $G$ is a holomorphically convex group of cohomological dimension two, we show that $G$ is isomorphic to the fundamental group of a compact Riemann surface. As a consequence, we show that if a linear group $G$ has (rational) cohomological dimension two and is the fundamental group of a smooth complex projective variety, then $G$ is a (virtual) surface group.

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BibTeX RIS

Indranil Biswas, Mahan Mj. 2014-02-26. Low dimensional projective groups. https://arxiv.org/abs/1203.4520

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