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

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dc.creatorCasnati, Gianfranco
dc.creatorNotari, Roberto
dc.date2008-05-26
dc.date.accessioned2026-07-07T09:40:54Z
dc.date.available2026-07-07T09:40:54Z
dc.descriptionLet $R$ be a local, Gorenstein ring with algebraically closed residue field $k$ of characteristic 0 and let $P_R(z):=\sum_{p=0}^{\infty}\dim_k(\tor_p^R(k,k))z^p$ 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.
dc.identifierhttps://arxiv.org/abs/0805.3899
dc.identifierhttp://arxiv.org/abs/0805.3899
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161643
dc.subjectCommutative Algebra
dc.subject13D40; 13H10
dc.titleThe Poincaré series of a local Gorenstein ring of multiplicity up to 10 is rational
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