### Abstract

This is a survey and research note on the modified Orlik conjecture derived from the division theorem introduced in Abe (Invent. Math. 204(1), 317–346, 2016). The division theorem is a generalization of classical addition-deletion theorems for free arrangements. The division theorem can be regarded as a modified converse of the Orlik’s conjecture with a combinatorial condition, i.e., an arrangement is free if the restriction is free and the characteristic polynomial of the restriction divides that of an arrangement. In this article we recall, summarize, pose and re-formulate some of results and problems related to the division theorem based on Abe (Invent. Math. 204(1), 317–346, 2016), and study the modified Orlik’s conjecture with partial answers.

Original language | English |
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Title of host publication | Perspectives in Lie Theory |

Editors | Filippo Callegaro, Giovanna Carnovale, Fabrizio Caselli, Corrado De Concini, Alberto De Sole |

Publisher | Springer International Publishing |

Pages | 389-401 |

Number of pages | 13 |

ISBN (Print) | 9783319589701 |

DOIs | |

Publication status | Published - Jan 1 2017 |

Event | INdAM Workshop on Perspectives in Lie Theory, 2015 - Pisa, Italy Duration: Dec 9 2014 → Feb 28 2015 |

### Publication series

Name | Springer INdAM Series |
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Volume | 19 |

ISSN (Print) | 2281-518X |

ISSN (Electronic) | 2281-5198 |

### Other

Other | INdAM Workshop on Perspectives in Lie Theory, 2015 |
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Country | Italy |

City | Pisa |

Period | 12/9/14 → 2/28/15 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Perspectives in Lie Theory*(pp. 389-401). (Springer INdAM Series; Vol. 19). Springer International Publishing. https://doi.org/10.1007/978-3-319-58971-8_14