TY - GEN
T1 - Restrictions of free arrangements and the division theorem
AU - Abe, Takuro
N1 - Funding Information:
Acknowledgements The author is grateful to the referee for the careful reading of this paper with a lot of important comments. This work is partially supported by JSPS Grants-in-Aid for Young Scientists (B) No. 24740012.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85038264699&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85038264699&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-58971-8_14
DO - 10.1007/978-3-319-58971-8_14
M3 - Conference contribution
AN - SCOPUS:85038264699
SN - 9783319589701
T3 - Springer INdAM Series
SP - 389
EP - 401
BT - Perspectives in Lie Theory
A2 - Callegaro, Filippo
A2 - Carnovale, Giovanna
A2 - Caselli, Fabrizio
A2 - De Concini, Corrado
A2 - De Sole, Alberto
PB - Springer International Publishing
T2 - INdAM Workshop on Perspectives in Lie Theory, 2015
Y2 - 9 December 2014 through 28 February 2015
ER -