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Free arrangements of hyperplanes and unitary reflection groups. (English) Zbl 0476.14016

MSC:
14J25 Special surfaces
13H15 Multiplicity theory and related topics
32B10 Germs of analytic sets, local parametrization
13C10 Projective and free modules and ideals in commutative rings
20G40 Linear algebraic groups over finite fields
20F05 Generators, relations, and presentations of groups
51A20 Configuration theorems in linear incidence geometry
05B30 Other designs, configurations
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[1] E. Brieskorn: Sur les groupes de tresses (d’apres V. I. Arnold). Seminaire Bourbaki 24e annee, 1971/72, no. 401. Lect. Notes in Math., vol. 317, Berlin-Heidelberg-New York, Springer (1973). · Zbl 0277.55003 · numdam:SB_1971-1972__14__21_0 · eudml:109814
[2] P. Orlik and L. Solomon: Combinatorics and topology of complements of hyperplanes. Invent. Math., 56, 167-189 (1980). · Zbl 0432.14016 · doi:10.1007/BF01392549 · eudml:142694
[3] P. Orlik and L. Solomon: Unitary reflection groups and cohomology. Ibid., 59, 77-94 (1980). · Zbl 0452.20050 · doi:10.1007/BF01390316 · eudml:142731
[4] K. Saito: On the uniformization of complements of discriminant loci. Symp. in Pure Math., Williams College, 1975, Providence, AMS (1977).
[5] K. Saito: Theory of logarithmic differential forms and logarithmic vector fields. J. Fac. Sci. Univ. Tokyo, Sect. IA, 27, 265-291 (1980). · Zbl 0496.32007
[6] G. C. Shepherd and J. A. Todd: Finite unitary reflection groups. Canad. J. Math., 6, 274-304 (1954). · Zbl 0055.14305 · doi:10.4153/CJM-1954-028-3
[7] H. Terao: Arrangements of hyperplanes and their freeness I. J. Fac. Sci. Univ. Tokyo, Sect. IA, 27, 293-312 (1980). · Zbl 0509.14006
[8] H. Terao: Generalized exponents of a free arrangement of hyperplanes and Shepherd-Todd-Brieskorn formula (to appear). · Zbl 0437.51002 · doi:10.1007/BF01389197 · eudml:142794
[9] H. Terao: On Betti numbers of complement of hyperplanes (to appear). · Zbl 0484.14004 · doi:10.2977/prims/1195185267
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