• Gianfranco Casnati

Articles written in Proceedings – Mathematical Sciences

• The Poincaré Series of a Local Gorenstein Ring of Multiplicity up to 10 is Rational

Let 𝑅 be a local, Gorenstein ring with algebraically closed residue field 𝑘 of characteristic 0 and let $P_R(z):=\sum^\infty_{p=0}\dim_k(\mathrm{Tor}^R_p(k, k))z^p$ 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.

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019