(Ir)reducibility

Martin Guest; Claus Hertling

doi:10.1007/978-3-319-66526-9_3

(Ir)reducibility

Martin Guest^*, Claus Hertling

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

A pair (H, ∇), where H → M is a holomorphic vector bundle on a complex manifold M, and ∇ is a (flat) meromorphic connection, is said to be reducible if there exists a subbundle G ⊂ H with 0 < rank G < rank H which is (at all nonsingular points of the connection) a flat subbundle. Such a G will simply be called a flat subbundle. A pair (H, ∇) is completely reducible if it decomposes into a sum of flat rank 1 subbundles.

Original language	English
Title of host publication	Lecture Notes in Mathematics
Publisher	Springer Verlag
Pages	33-36
Number of pages	4
Volume	2198
DOIs	https://doi.org/10.1007/978-3-319-66526-9_3
Publication status	Published - 2017

Publication series

Name	Lecture Notes in Mathematics
Volume	2198
ISSN (Print)	0075-8434

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/978-3-319-66526-9_3

Cite this

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abstract = "A pair (H, ∇), where H → M is a holomorphic vector bundle on a complex manifold M, and ∇ is a (flat) meromorphic connection, is said to be reducible if there exists a subbundle G ⊂ H with 0 < rank G < rank H which is (at all nonsingular points of the connection) a flat subbundle. Such a G will simply be called a flat subbundle. A pair (H, ∇) is completely reducible if it decomposes into a sum of flat rank 1 subbundles.",

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AB - A pair (H, ∇), where H → M is a holomorphic vector bundle on a complex manifold M, and ∇ is a (flat) meromorphic connection, is said to be reducible if there exists a subbundle G ⊂ H with 0 < rank G < rank H which is (at all nonsingular points of the connection) a flat subbundle. Such a G will simply be called a flat subbundle. A pair (H, ∇) is completely reducible if it decomposes into a sum of flat rank 1 subbundles.

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(Ir)reducibility

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