TY - JOUR

T1 - Multiple addition, deletion and restriction theorems for hyperplane arrangements

AU - Abe, Takuro

AU - Terao, Hiroaki

N1 - Funding Information:
Received by the editors January 22, 2018, and, in revised form, February 10, 2019. 2010 Mathematics Subject Classification. Primary 32S22; Secondary 52C35. Key words and phrases. Hyperplane arrangements, free arrangements, addition-deletion and restriction theorems, Catalan arrangements. The first author was partially supported by KAKENHI, JSPS Grant-in-Aid for Scientific Research (B) 16H03924, and Grant-in-Aid for Exploratory Research 16K13744.

PY - 2019

Y1 - 2019

N2 - In the study of free arrangements, the most useful result to construct/ check free arrangements is the addition-deletion theorem in [J. Fac. Sci. Univ. Tokyo 27 (1980), 293-320]. Recently, the multiple version of the addition theorem was proved in [J. Eur. Math. Soc. 18 (2016), 1339-1348], called the multiple addition theorem (MAT), to prove the ideal-free theorem. The aim of this article is to give the deletion version of MAT, the multiple deletion theorem (MDT). Also, we can generalize MAT to get MAT2 from the viewpoint of our new proof. Moreover, we introduce the restriction version, a multiple restriction theorem (MRT). Applications of MAT2, including the combinatorial freeness of the extended Catalan arrangements, are given.

AB - In the study of free arrangements, the most useful result to construct/ check free arrangements is the addition-deletion theorem in [J. Fac. Sci. Univ. Tokyo 27 (1980), 293-320]. Recently, the multiple version of the addition theorem was proved in [J. Eur. Math. Soc. 18 (2016), 1339-1348], called the multiple addition theorem (MAT), to prove the ideal-free theorem. The aim of this article is to give the deletion version of MAT, the multiple deletion theorem (MDT). Also, we can generalize MAT to get MAT2 from the viewpoint of our new proof. Moreover, we introduce the restriction version, a multiple restriction theorem (MRT). Applications of MAT2, including the combinatorial freeness of the extended Catalan arrangements, are given.

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U2 - 10.1090/proc/14592

DO - 10.1090/proc/14592

M3 - Article

AN - SCOPUS:85073037637

VL - 147

SP - 4835

EP - 4845

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -