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

Proceedings Mathematical Sciences

Gianfranco Casnati²  Roberto Notari¹ 

[1] Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, via Bonardi , 0 Milano, Italy$$;Dipartimento di Matematica, Politecnico di Torino, c.so Duca degli Abruzzi , 0 Torino, Italy$$

关键词: Gorenstein;    Artinian;    Poincaré series.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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

【 授权许可】

Unknown