### 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 |
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Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer Verlag |

Pages | 33-36 |

Number of pages | 4 |

Volume | 2198 |

DOIs | |

Publication status | Published - 2017 |

### Publication series

Name | Lecture Notes in Mathematics |
---|---|

Volume | 2198 |

ISSN (Print) | 0075-8434 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Lecture Notes in Mathematics*(Vol. 2198, pp. 33-36). (Lecture Notes in Mathematics; Vol. 2198). Springer Verlag. https://doi.org/10.1007/978-3-319-66526-9_3

**(Ir)reducibility.** / Guest, Martin; Hertling, Claus.

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

*Lecture Notes in Mathematics.*vol. 2198, Lecture Notes in Mathematics, vol. 2198, Springer Verlag, pp. 33-36. https://doi.org/10.1007/978-3-319-66526-9_3

}

TY - CHAP

T1 - (Ir)reducibility

AU - Guest, Martin

AU - Hertling, Claus

PY - 2017

Y1 - 2017

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85031995808&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031995808&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-66526-9_3

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

M3 - Chapter

AN - SCOPUS:85031995808

VL - 2198

T3 - Lecture Notes in Mathematics

SP - 33

EP - 36

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -