Poincaré series for curve singularities and its behaviour under projections
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Title
Poincaré series for curve singularities and its behaviour under projectionsAuthor (s)
Date
2015Publisher
ElsevierISSN
0022-4049Bibliographic citation
MOYANO-FERNÁNDEZ, Julio José. Poincaré series for curve singularities and its behaviour under projections. Journal of Pure and Applied Algebra, 2015, vol. 219, no 6, p. 2449-2462.Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0022404914002473Version
info:eu-repo/semantics/sumittedVersionSubject
Abstract
Let O be an equicharacteristic reduced complete noetherian local ring of Krull dimension one, and let S be the value semigroup associated with O. The aim of the paper is to investigate the behaviour of the multi-v ... [+]
Let O be an equicharacteristic reduced complete noetherian local ring of Krull dimension one, and let S be the value semigroup associated with O. The aim of the paper is to investigate the behaviour of the multi-variable Poincaré series associated to S with respect to the property of “forgetting variables”. We prove that, for O Gorenstein, the Poincaré series with one less variable can be explicitly computed in terms of the original series; this provides also a shorter and pure arithmetical way to show that the Poincaré series is a complete invariant of the equisingularity. Moreover we express (without the Gorenstein assumption) the Hilbert series of S in terms of the Poincaré series of the unions of irreducible components of the singularity. [-]
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Journal of Pure and Applied Algebra, 2015, vol. 219, no 6Rights
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