The Poincaré series of a local Gorenstein ring of multiplicity up to 10 is rational

2008/05/26 by Gianfranco Casnati, Casnati, Gianfranco, Roberto Notari +1
Mathematics · #13D40 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D40 #msc:13H10

paper · pdf · doi:10.48550/arxiv.0805.3899

arxiv created 2008/05/26 · arxiv updated 2009/12/01

Abstract

Let R be a local, Gorenstein ring with algebraically closed residue field k of characteristic 0 and let P_R(z):=∑_p=0^∞dim_k(\tor_p^R(k,k))z^p be its Poincaré series. We compute P_R when R belongs to a particular class defined in the introduction, proving its rationality. As a by--product we prove the rationality of P_R for all local, Gorenstein rings of multiplicity at most 10.

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