Restrictions of free arrangements and the division theorem

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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 languageEnglish
Title of host publicationPerspectives in Lie Theory
EditorsFilippo Callegaro, Giovanna Carnovale, Fabrizio Caselli, Corrado De Concini, Alberto De Sole
PublisherSpringer International Publishing
Pages389-401
Number of pages13
ISBN (Print)9783319589701
DOIs
Publication statusPublished - Jan 1 2017
EventINdAM Workshop on Perspectives in Lie Theory, 2015 - Pisa, Italy
Duration: Dec 9 2014Feb 28 2015

Publication series

NameSpringer INdAM Series
Volume19
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

Other

OtherINdAM Workshop on Perspectives in Lie Theory, 2015
CountryItaly
CityPisa
Period12/9/142/28/15

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Abe, T. (2017). Restrictions of free arrangements and the division theorem. In F. Callegaro, G. Carnovale, F. Caselli, C. De Concini, & A. De Sole (Eds.), 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