Standard Bases for fractional ideals of the local ring of an algebroid curve

In this paper we present an algorithm to compute a Standard Basis for a fractional ideal I of the local ring O of an n-space algebroid curve with several branches. This allows us to determine the semimodule of values of I. When I=O, we may obtain a (finite) set of generators of the semiring of value...

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Bibliographic Details
Published in:Journal of algebra 2020-06, Vol.551, p.342-361
Main Authors: Carvalho, E., Hernandes, M.E.
Format: Article
Language:English
Subjects:
Algebroid curves
Semiring and semimodules of values
Standard Bases
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Summary:In this paper we present an algorithm to compute a Standard Basis for a fractional ideal I of the local ring O of an n-space algebroid curve with several branches. This allows us to determine the semimodule of values of I. When I=O, we may obtain a (finite) set of generators of the semiring of values of the curve, which determines its classical semigroup. In the complex context, identifying the Kähler differential module ΩO/C of a plane curve with a fractional ideal of O and applying our algorithm, we can compute the set of values of ΩO/C, which is an important analytic invariant associated to the curve.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2020.01.018