β nbc-bases for cohomology of local systems on hyperplane complements

Michael J Falk, Hiroaki Terao

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

We study cohomology with coefficients in a rank one local system on the complement of an arrangement of hyperplanes A. The cohomology plays an important role for the theory of generalized hypergeometric functions. We combine several known results to construct explicit bases of logarithmic forms for the only non-vanishing cohomology group, under some nonresonance conditions on the local system, for any arrangement A. The bases are determined by a linear ordering of the hyperplanes, and are indexed by certain "no-broken-circuits" bases of A. The basic forms depend on the local system, but any two bases constructed in this way are related by a matrix of integer constants which depend only on the linear orders and not on the local system. In certain special cases we show the existence of bases of monomial logarithmic forms.

Original languageEnglish (US)
Pages (from-to)189-202
Number of pages14
JournalTransactions of the American Mathematical Society
Volume349
Issue number1
StatePublished - 1997

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Local System
Hyperplane
Cohomology
Complement
Networks (circuits)
Logarithmic
Arrangement of Hyperplanes
Generalized Hypergeometric Function
Linear Ordering
Nonresonance
Cohomology Group
Monomial
Linear Order
Arrangement
Integer
Coefficient
Form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

β nbc-bases for cohomology of local systems on hyperplane complements. / Falk, Michael J; Terao, Hiroaki.

In: Transactions of the American Mathematical Society, Vol. 349, No. 1, 1997, p. 189-202.

Research output: Contribution to journalArticle

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