Poincaré series for curve singularities and its behaviour under projections
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Julio José Moyano-Fernández [1]
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[1] Universidad Jaume I, Spain
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- Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 6 (June 2015), 2015, págs. 2449-2462
- Idioma: inglés
- DOI: 10.1016/j.jpaa.2014.09.009
- Enlaces
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Resumen
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.
