Efficient computation of resonance varieties via Grassmannians

Paulo Lima-Filho, Hal Schenck

Research output: Contribution to journalArticlepeer-review

Abstract

Associated to the cohomology ring A of the complement X (A) of a hyperplane arrangement A in C are the resonance varieties Rk (A). The most studied of these is R1 (A), which is the union of the tangent cones at 1 to the characteristic varieties of π1 (X (A)). R1 (A) may be described in terms of Fitting ideals, or as the locus where a certain E x t module is supported. Both these descriptions give obvious algorithms for computation. In this note, we show that interpreting R1 (A) as the locus of decomposable two-tensors in the Orlik-Solomon ideal of A leads to a description of R1 (A) as the intersection of a Grassmannian with a linear space, determined by the quadratic generators of the Orlik-Solomon ideal. This method is much faster than previous alternatives.

Original languageEnglish (US)
Pages (from-to)1606-1611
Number of pages6
JournalJournal of Pure and Applied Algebra
Volume213
Issue number8
DOIs
StatePublished - Aug 2009
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory

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