Standard Bases for Fractional Ideals of the Local Ring of an Algebroid\n Curve

2019/03/11 by Emilio Carvalho, Carvalho, Emilio, Marcelo Escudeiro Hernandes +1 · 1 citation
Computer Science · Mathematics · Medicine · #14H20 and 13P10 (secondary) #14H50 (primary) #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Spinal Hematomas and Complications

paper · pdf · doi:10.48550/arxiv.1903.04696

openalex publication_date 2019/03/11 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

In this paper we present an algorithm to compute a Standard Basis for a\nfractional ideal \I of the local ring \O of an n-space\nalgebroid curve with several branches. This allows us to determine the\nsemimodule of values of \I. When \I=\O, we may\nobtain a (finite) set of generators of the semiring of values of the curve,\nwhich determines its classical semigroup. In the complex context, identifying\nthe K "ahler differential module \Ω_\O/\ℂ of a plane\ncurve with a fractional ideal of \O and applying our algorithm, we\ncan compute the set of values of \Ω_\O/\ℂ, which is an\nimportant analytic invariant associated to the curve.\n

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