Holonomy groups of stable vector bundles

V. Balaji, János Kollár

Research output: Contribution to journalArticle

16 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 languageEnglish (US)
Pages (from-to)183-211
Number of pages29
JournalPublications of the Research Institute for Mathematical Sciences
Volume44
Issue number2
DOIs
StatePublished - May 1 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Holonomy group
  • Parabolic bundle
  • Stability
  • Vector bundle

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