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

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/119/04/0459-0468

• # Keywords

Gorenstein; Artinian; Poincaré series.

• # Abstract

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.

• # Author Affiliations

1. Dipartimento di Matematica, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129 Torino, Italy
2. Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019