Algebras generated by reciprocals of linear forms

2001/05/31 by Hiroaki Terao · 2 citations
Mathematics · #math.CO #math.AC #math.AG #msc:32S22 #msc:13D40 #msc:13N10 #msc:52C35

paper · pdf

published as Journal of Algebra, vol. 250, 549-558 (2002) · a typo corrected; a footnote added

arxiv created 2001/12/04 · arxiv updated 2009/11/30

Abstract

Let Δ be a finite set of nonzero linear forms in several variables with coefficients in a field \mathbf K of characteristic zero. Consider the \mathbf K-algebra C(Δ) of rational functions generated by \1/α| α∈ Δ\. Then the ring ∂(V) of differential operators with constant coefficients naturally acts on C(Δ). We study the graded ∂(V)-module structure of C(Δ). We especially find standard systems of minimal generators and a combinatorial formula for the Poincaré series of C(Δ). Our proofs are based on a theorem by Brion-Vergne [brv1] and results by Orlik-Terao [ort2.

Cited by

• Vanishing theorems for combinatorial geometries
• The geometry of zonotopal algebras II: Orlik--Terao algebras and Schubert varieties

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