2019-03-23T02:45:28Zhttp://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/1594982017-02-20T23:49:09Zcom_10234_7037com_10234_9col_10234_8635
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Moyano Fernández, Julio José
author
2015
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.
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.
0022-4049
http://hdl.handle.net/10234/159498
http://dx.doi.org/10.1016/j.jpaa.2014.09.009
curve singularity
Poincaré series
value semigroup
Grothendieck ring of varieties
motivic integration
Alexander polynomial
Poincaré series for curve singularities and its behaviour under projections