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Generalized exponents of a free arrangement of hyperplanes and Shepherd- Todd-Brieskorn formula. (English) Zbl 0437.51002

MSC:
51A40 Translation planes and spreads in linear incidence geometry
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References:
[1] Brieskorn, E.: Sur les groupes de tresses (d’après V.I. Arnold), Séminaire Bourbaki 24e année 1971/72. Springer Lecture Notes No. 317, Berlin-Heidelberg-New York: Springer 1973
[2] Coxeter, H.S.M.: The product of generators of a finite group generated by reflections. Duke Math. J.18, 765-782 (1951) · Zbl 0044.25603 · doi:10.1215/S0012-7094-51-01870-4
[3] Deligne, P.: Théorie de Hodge II. Publ. I.H.E.S.40, 5-57 (1972) · Zbl 0219.14007
[4] Matsumura, H.: Commutative Algebra, New York: Benjamin 1970 · Zbl 0211.06501
[5] Orlik, P., Solomon, L.: Combinatorics and topology of complements of hyperplanes. Inventiones math.56, 167-189 (1980) · Zbl 0432.14016 · doi:10.1007/BF01392549
[6] Orlik, P., Solomon, L.: Unitary reflection groups and cohomology. Inventiones math.59, 77-94 (1980) · Zbl 0452.20050 · doi:10.1007/BF01390316
[7] Saito, K.: On the uniformization of complements of discriminant loci. Symp. in Pure Math., Williams College, 1975, Providence: AMS 1977
[8] Saito, K.: Theory of logarithmic differential forms and logarithmic vector fields. J. Fac. Sci. Univ. Tokyo Sect. IA Math.27, 265-291 (1980) · Zbl 0496.32007
[9] Serre, J.P.: Algèbre locale multiplicités. Springer Lecture Notes No. 11, Berlin-Heidelberg-New York: Springer 1965
[10] Shepherd, G.C., Todd, J.A.: Finite unitary reflection groups. Canad. J. Math.6, 274-304 (1954) · Zbl 0055.14305 · doi:10.4153/CJM-1954-028-3
[11] Terao, H.: Arrangements of hyperplanes and their freeness I. J. Fac. Sci. Univ. Tokyo Sect. IA Math.27, 293-312 (1980) · Zbl 0509.14006
[12] Terao, H.: Arrangements of hyperplanes and their freeness II?the Coxeter equality. J. Fac. Sci. Univ. Tokyo Sect. IA Math.27, 313-320 (1980) · Zbl 0509.14007
[13] Terao, H.: Free arrangements and unitary reflection groups. Proc. Japan Acad. Ser. A,56, 389-392 (1980) · Zbl 0476.14016 · doi:10.3792/pjaa.56.389
[14] Zaslavsky, T.: Facing up to arrangements: face-count formulas for partitions of space by hyperplanes. Memoirs of the Amer. Math. Soc. No. 154, Providence: AMS 1975 · Zbl 0296.50010
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