%0 Journal Article
%T The Poincar¨¦ series of a local Gorenstein ring of multiplicity up to 10 is rational
%A Gianfranco Casnati
%A Roberto Notari
%J Mathematics
%D 2008
%I arXiv
%X Let $R$ 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 Poincar\'e 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.
%U http://arxiv.org/abs/0805.3899v1