Local Gröbner fan: polyhedral and computational approach

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The goal of this paper is to show that the local Gröbner fan is a polyhedral fan for ideals in the ring of power series and the homogenized ring of analytic differential operators. We will also discuss about relations between the local Gröbner fan and the (global) Gröbner fan for a given ideal and algorithms of computing local Gröbner fans. In rings of differential operators, finiteness and convexity of local Gröbner fans were firstly proved by Assi, Castro-Jiménez and Granger. But they did not prove that they are polyhedral fans.
34 pages, 2 figures. Version 2: mainly, we corrected the definition of the Newton polyhedron in 3.3

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Algebraic Geometry, Commutative Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/100964

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0412044
 http://arxiv.org/abs/math/0412044

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arXiv