Exponents of 2-multiarrangements and multiplicity lattices
Takuro Abe
and Yasuhide Numata
DOI: 10.1007/s10801-011-0291-7
Abstract
We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.
Pages: 1–17
Keywords: keywords hyperplane arrangements; multiarrangements; exponents of derivation modules; multiplicity lattices
Full Text: PDF
References
1. Abe, T.: The stability of the family of A2-type arrangements. J. Math. Kyoto Univ. 46(3), 617-636 (2006)
2. Abe, T.: Free and non-free multiplicity on the deleted A3 arrangement. Proc. Jpn. Acad., Ser. A 83(7), 99-103 (2007)
3. Abe, T.: The stability of the family of B2-type arrangements. Commun. Algebra 37(4), 1193-1215 (2009)
4. Abe, T.: Exponents of 2-multiarrangements and freeness of 3-arrangements (2010).
5. Abe, T., Terao, H., Wakefield, M.: The characteristic polynomial of a multiarrangement. Adv. Math. 215, 825-838 (2007)
6. Abe, T., Terao, H., Wakefield, M.: The e-multiplicity and addition-deletion theorems for multiarrangements. J. Lond. Math. Soc. 77(2), 335-348 (2008)
7. Orlik, P., Terao, H.: Arrangements of Hyperplanes. Grundlehren der Mathematischen Wissenschaften, vol.
300. Springer, Berlin (1992)
8. Saito, K.: Theory of logarithmic differential forms and logarithmic vector fields. J. Fac. Sci., Univ. Tokyo, Sect. IA Math 27, 265-291 (1980)
9. Terao, H.: Multiderivations of Coxeter arrangements. Invent. Math. 148, 659-674 (2002)
10. Wakamiko, A.: On the exponents of 2-multiarrangements. Tokyo J. Math. 30(1), 99-116 (2007)
11. Wakamiko, A.: Bases for the derivation modules of two-dimensional multi-Coxeter arrangements and universal derivations. Hokkaido Math. J. (to appear).
12. Wakefield, M., Yuzvinsky, S.: Derivations of an effective divisor on the complex projective line. Trans. Am. Math. Soc. 359, 4389-4403 (2007)
13. Yoshinaga, M.: The primitive derivation and freeness of multi-Coxeter arrangements. Proc. Jpn. Acad., Ser. A 78(7), 116-119 (2002)
14. Yoshinaga, M.: Characterization of a free arrangement and conjecture of Edelman and Reiner. Invent.
2. Abe, T.: Free and non-free multiplicity on the deleted A3 arrangement. Proc. Jpn. Acad., Ser. A 83(7), 99-103 (2007)
3. Abe, T.: The stability of the family of B2-type arrangements. Commun. Algebra 37(4), 1193-1215 (2009)
4. Abe, T.: Exponents of 2-multiarrangements and freeness of 3-arrangements (2010).
5. Abe, T., Terao, H., Wakefield, M.: The characteristic polynomial of a multiarrangement. Adv. Math. 215, 825-838 (2007)
6. Abe, T., Terao, H., Wakefield, M.: The e-multiplicity and addition-deletion theorems for multiarrangements. J. Lond. Math. Soc. 77(2), 335-348 (2008)
7. Orlik, P., Terao, H.: Arrangements of Hyperplanes. Grundlehren der Mathematischen Wissenschaften, vol.
300. Springer, Berlin (1992)
8. Saito, K.: Theory of logarithmic differential forms and logarithmic vector fields. J. Fac. Sci., Univ. Tokyo, Sect. IA Math 27, 265-291 (1980)
9. Terao, H.: Multiderivations of Coxeter arrangements. Invent. Math. 148, 659-674 (2002)
10. Wakamiko, A.: On the exponents of 2-multiarrangements. Tokyo J. Math. 30(1), 99-116 (2007)
11. Wakamiko, A.: Bases for the derivation modules of two-dimensional multi-Coxeter arrangements and universal derivations. Hokkaido Math. J. (to appear).
12. Wakefield, M., Yuzvinsky, S.: Derivations of an effective divisor on the complex projective line. Trans. Am. Math. Soc. 359, 4389-4403 (2007)
13. Yoshinaga, M.: The primitive derivation and freeness of multi-Coxeter arrangements. Proc. Jpn. Acad., Ser. A 78(7), 116-119 (2002)
14. Yoshinaga, M.: Characterization of a free arrangement and conjecture of Edelman and Reiner. Invent.
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