2004/12/02 by Rouchdi Bahloul, Bahloul, Rouchdi, Nobuki Takayama +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.math/0412044
openalex publication_date 2004/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.