An Algorithm to Construct A Basis for the Module of Logarithmic Vector Fields

2007/06/29 by Yasuhide Numata, Numata, Yasuhide · 1 citation
Computer Science · Engineering · Mathematics · #32S22 #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.0707.0004

openalex publication_date 2007/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider logarithmic vector fields parametrized by finite collections of weighted hyperplanes. For a finite collection of weighted hyperplanes in a two-dimensional vector space, it is known that the set of such vector fields is a free module of rank two whose basis elements are homogeneous. We give an algorithm to construct a homogeneous basis for the module.

Cited by

• Exponents of 2-multiarrangements of three lines over fields of positive characteristic

Related

• A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups
• Free resolution of the logarithmic derivation modules of close to free arrangements
• Logarithmic vector fields and multiplication table
• The Computation of the Logarithmic Cohomology for Plane Curves
• Logarithmic vector fields along smooth divisors in projective spaces