Algebras generated by reciprocals of linear forms
| dc.creator | Terao, Hiroaki | |
| dc.date | 2001-05-11 | |
| dc.date | 2001-12-04 | |
| dc.date.accessioned | 2026-07-07T04:41:40Z | |
| dc.date.available | 2026-07-07T04:41:40Z | |
| dc.description | 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 $\{1/α\mid α\in Δ\}$. Then the ring $\partial(V)$ of differential operators with constant coefficients naturally acts on $C(Δ)$. We study the graded $\partial(V)$-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}. | |
| dc.description | a typo corrected; a footnote added | |
| dc.identifier | https://arxiv.org/abs/math/0105095 | |
| dc.identifier | http://arxiv.org/abs/math/0105095 | |
| dc.identifier | Journal of Algebra, vol. 250, 549-558 (2002) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61452 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32S22;13D40;13N10;52C35 | |
| dc.title | Algebras generated by reciprocals of linear forms | |
| dc.type | text |