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Logarithmic forms on affine arrangements

  • Hiroaki Terao (a1) and Sergey Yuzvinsky (a2)
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Let V be an affine of dimension l over some field K. An arrangement A is a finite collection of affine hyperplanes in V. We call A an l-arrangement when we want to emphasize the dimension of V. We use [6] as a general reference. Choose an arbitrary point of V and fix it throughout this paper. We will use it as the origin.

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References
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[ 1 ] Aomoto K., Les équations aux différences linéaires et les intégrales des fonctions multiformes, J. Fac. Sci. Univ. Tokyo, Sec. IA, 22 (1975), 271297.
[ 2 ] Aomoto K., On the structure of integrals of power products of linear functions, Sci. Papers, Coll. Gen. Educ. Univ. Tokyo, 27 (1977), 4961.
[ 3 ] Aomoto K., Hypergeometric functions, the past, today, and… (from complex analytic view point), (in Japanese) in Sûgaku, 45 (1993), 208220.
[ 4 ] Aomoto K., Kita M., Orlik P., Terao H., Twisted de Rham cohomology groups of logarithmic forms, to appear in Advances in Math.
[ 5 ] Gelfand I. M., Zelevinsky A. V., Algebraic and combinatorial aspects of the general theory of hypergeometric functions, Funct. Anal, and Appl., 20 (1986), 183197.
[ 6 ] Orlik P., Terao H., Arrangements of hyperplanes. Grundlehren der math. Wiss. 300, Springer-Verlag, Berlin-Heidelberg-New York, 1992.
[ 7 ] Orlik P., Terao H., Arrangements and Milnor fibers, Math. Ann., 301 (1995), 211235.
[ 8 ] Saito K., Theory of logarithmic differential forms and logarithmic vector fields, J. Fac. Sci. Univ. Tokyo Sec. 1A, 27 (1980), 266291.
[ 9 ] Solomon L., Terao H., A formula for the characteristic polynomial of an arrangement, Adv. in Math., 64 (1987), 305325.
[10] Terao H., Generalized exponents of a free arrangement of hyperplanes and Shephard-Todd-Brieskorn formula, Invent, math., 63 (1981), 159179.
[11] Yuzvinsky S., First two obstructions to the freeness of arrangements, Trans. AMS, 335 (1993), 231244.
[12] Varchenko A., Multidimensional hypergeometric functions and the representation theory of Lie algebras and quantum groups, World Scientific Publishers, 1995.
[13] Ziegler G., Combinatorial construction of logarithmic differential forms. Adv. in Math., 76 (1989), 116154.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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