Free and non-free multiplicity on the deleted $A_{3}$ arrangement
Takuro Abe
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 83, Number 7
(2007), 99-103.
Abstract
We give the first complete classification of free and non-free multiplicities on an arrangement, called the deleted $A_{3}$ arrangement, which admits both of them.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pja/1200672008
Mathematical Reviews number (MathSciNet): MR2361419
Digital Object Identifier: doi:10.3792/pjaa.83.99
Zentralblatt MATH identifier: 1158.32012
References
T. Abe, H. Terao and M. Wakefield, The characteristic polynomial of a multiarrangement, Adv. in Math. 215 (2007), 825--838. arxiv math.AC/0611742.
Mathematical Reviews (MathSciNet): MR2355609
Digital Object Identifier: doi:10.1016/j.aim.2007.04.019
Zentralblatt MATH: 1123.52012
T. Abe, H. Terao and M. Wakefield, The $e$-multiplicity and addition-deletion theorems for multiarrangements. arxiv math.CV/0612739.
P. Orlik and H. Terao, Arrangements of hyperplanes, Grundlehren der Mathematischen Wissenschaften, 300. Springer-Verlag, Berlin, 1992.
Mathematical Reviews (MathSciNet): MR1217488
Zentralblatt MATH: 0757.55001
A. Wakamiko, On the Exponents of 2-Multiarrangements. Tokyo J. Math. 30 (2007), no.1, 99--116.
Mathematical Reviews (MathSciNet): MR2328057
Digital Object Identifier: doi:10.3836/tjm/1184963649
Project Euclid: euclid.tjm/1184963649
Zentralblatt MATH: 1130.52010
M. Yoshinaga, Characterization of a free arrangement and conjecture of Edelman and Reiner, Invent. Math. 157 (2004), no.2, 449--454.
Mathematical Reviews (MathSciNet): MR2077250
Digital Object Identifier: doi:10.1007/s00222-004-0359-2
Zentralblatt MATH: 1113.52039
M. Yoshinaga, On the freeness of 3-arrangements, Bull. London Math. Soc. 37 (2005), no.1, 126--134.
Mathematical Reviews (MathSciNet): MR2105827
Digital Object Identifier: doi:10.1112/S0024609304003704
Zentralblatt MATH: 1071.52019
M. Yoshinaga, Characterizations of free arrangements, Kyoudai suuriken-Kokyuroku ``Geometry and analysis on complex algebraic varieties''. (to appear).
G. M. Ziegler, Multiarrangements of hyperplanes and their freeness, in Singularities (Iowa City, IA, 1986), 345--359, Contemp. Math., 90, Amer. Math. Soc., Providence, RI, 1989.
Mathematical Reviews (MathSciNet): MR1000610
Zentralblatt MATH: 0678.51010
Proceedings of the Japan Academy, Series A, Mathematical Sciences
