Hostname: page-component-5cf477f64f-n7lw4 Total loading time: 0 Render date: 2025-04-07T13:58:51.730Z Has data issue: false hasContentIssue false
  • English
  • Français

Logarithmic forms on affine arrangements

Published online by Cambridge University Press:  22 January 2016

Hiroaki Terao  and
Sergey Yuzvinsky
Hiroaki Terao
Affiliation:
Mathematics Department, University of Wisconsin, Madison, WI 53706
Sergey Yuzvinsky
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 139 , September 1995 , pp. 129 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

References

[ 1 ] Aomoto, K., Les équations aux différences linéaires et les intégrales des fonctions multiformes, J. Fac. Sci. Univ. Tokyo, Sec. IA, 22 (1975), 271–297.Google Scholar
[ 2 ] Aomoto, K., On the structure of integrals of power products of linear functions, Sci. Papers, Coll. Gen. Educ. Univ. Tokyo, 27 (1977), 49–61.Google Scholar
[ 3 ] Aomoto, K., Hypergeometric functions, the past, today, and… (from complex analytic view point), (in Japanese) in Sûgaku, 45 (1993), 208–220.Google Scholar
[ 4 ] Aomoto, K., Kita, M., Orlik, P., Terao, H., Twisted de Rham cohomology groups of logarithmic forms, to appear in Advances in Math.Google Scholar
[ 5 ] Gelfand, I. M., Zelevinsky, A. V., Algebraic and combinatorial aspects of the general theory of hypergeometric functions, Funct. Anal, and Appl., 20 (1986), 183–197.Google Scholar
[ 6 ] Orlik, P., Terao, H., Arrangements of hyperplanes. Grundlehren der math. Wiss. 300, Springer-Verlag, Berlin-Heidelberg-New York, 1992.Google Scholar
[ 7 ] Orlik, P., Terao, H., Arrangements and Milnor fibers, Math. Ann., 301 (1995), 211–235.CrossRefGoogle Scholar
[ 8 ] Saito, K., Theory of logarithmic differential forms and logarithmic vector fields, J. Fac. Sci. Univ. Tokyo Sec. 1A, 27 (1980), 266–291.Google Scholar
[ 9 ] Solomon, L., Terao, H., A formula for the characteristic polynomial of an arrangement, Adv. in Math., 64 (1987), 305–325.CrossRefGoogle Scholar
[10] Terao, H., Generalized exponents of a free arrangement of hyperplanes and Shephard-Todd-Brieskorn formula, Invent, math., 63 (1981), 159–179.Google Scholar
[11] Yuzvinsky, S., First two obstructions to the freeness of arrangements, Trans. AMS, 335 (1993), 231–244.Google Scholar
[12] Varchenko, A., Multidimensional hypergeometric functions and the representation theory of Lie algebras and quantum groups, World Scientific Publishers, 1995.CrossRefGoogle Scholar
[13] Ziegler, G., Combinatorial construction of logarithmic differential forms. Adv. in Math., 76 (1989), 116–154.Google Scholar