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De Rham cohomology of logarithmic forms on arrangements of hyperplanes
Author(s):
Jonathan
Wiens;
Sergey
Yuzvinsky
Journal:
Trans. Amer. Math. Soc.
349
(1997),
1653-1662.
MSC (1991):
Primary 52B30, 14F40, 05B35
MathSciNet review:
1407505
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Abstract:
The paper is devoted to computation of the cohomology of the complex of logarithmic differential forms with coefficients in rational functions whose poles are located on the union of several hyperplanes of a linear space over a field of characteristic zero. The main result asserts that for a vast class of hyperplane arrangements, including all free and generic arrangements, the cohomology algebra coincides with the Orlik-Solomon algebra. Over the field of complex numbers, this means that the cohomologies coincide with the cohomologies of the complement of the union of the hyperplanes. We also prove that the cohomologies do not change if poles of arbitrary multiplicity are allowed on some of the hyperplanes. In particular, this gives an analogue of the algebraic de Rham theorem for an arbitrary arrangement over an arbitrary field of zero characteristic.
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Additional Information:
Jonathan
Wiens
Affiliation:
Department of Mathematical Sciences, University of Alaska, Fairbanks, Alaska 99775
Sergey
Yuzvinsky
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403
DOI:
10.1090/S0002-9947-97-01894-1
PII:
S 0002-9947(97)01894-1
Received by editor(s):
November 15, 1994
Copyright of article:
Copyright
1997,
American Mathematical Society
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