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 ):= Σ p =0 ∞ dim k (Tor p R ( 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...

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Bibliographic Details
Published in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2009-09, Vol.119 (4), p.459-468
Main Authors: Casnati, Gianfranco, Notari, Roberto
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:Let R be a local, Gorenstein ring with algebraically closed residue field k of characteristic 0 and let P R ( z ):= Σ p =0 ∞ dim k (Tor p R ( 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.
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-009-0041-0