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

Gianfranco Casnati, Roberto Notari

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 Poincaré se…