Holonomy groups of stable vector bundles

V. Balaji; János Kollár

doi:10.2977/prims/1210167326

Holonomy groups of stable vector bundles

V. Balaji, János Kollár

Mathematics

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21 Scopus citations

Abstract

We define the notion of holonomy group for a stable vector bundle F on a variety in terms of the Narasimhan-Seshadri unitary representation of its restriction to curves. Next we relate the holonomy group to the minimal structure group and to the decomposition of tensor powers of F. Finally we illustrate the principle that either the holonomy is large or there is a clear geometric reason why it should be small.

Original language	English (US)
Pages (from-to)	183-211
Number of pages	29
Journal	Publications of the Research Institute for Mathematical Sciences
Volume	44
Issue number	2
DOIs	https://doi.org/10.2977/prims/1210167326
State	Published - May 2008

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Holonomy group
Parabolic bundle
Stability
Vector bundle

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abstract = "We define the notion of holonomy group for a stable vector bundle F on a variety in terms of the Narasimhan-Seshadri unitary representation of its restriction to curves. Next we relate the holonomy group to the minimal structure group and to the decomposition of tensor powers of F. Finally we illustrate the principle that either the holonomy is large or there is a clear geometric reason why it should be small.",

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AU - Balaji, V.

AU - Kollár, János

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AB - We define the notion of holonomy group for a stable vector bundle F on a variety in terms of the Narasimhan-Seshadri unitary representation of its restriction to curves. Next we relate the holonomy group to the minimal structure group and to the decomposition of tensor powers of F. Finally we illustrate the principle that either the holonomy is large or there is a clear geometric reason why it should be small.

KW - Holonomy group

KW - Parabolic bundle

KW - Stability

KW - Vector bundle

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Holonomy groups of stable vector bundles

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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