On meromorphic functions defined by a differential system of order 1, II

2006/05/31 by Tristan Torrelli, Torrelli, Tristan · 2 citations
Mathematics · #14F10 #14F40 #32C38 #32S25 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #math.AG #msc:14F10 #msc:14F40 #msc:32C38 #msc:32S25

paper · pdf · doi:10.48550/arxiv.math/0605787

28 pages, 1 diagram

arxiv created 2006/05/31 · openalex publication_date 2006/05/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a nonzero germ h of holomorphic function on (Cⁿ,0), we study the condition: ``the ideal Ann_D 1/h is generated by operators of order 1''. When h defines a generic arrangement of hypersurfaces with an isolated singularity, we show that it is verified if and only if h is weighted homogeneous and -1 is the only integral root of its Bernstein-Sato polynomial. When h is a product, we give a process to test this last condition. Finally, we study some other related conditions.

Cited by

• Advances on a conjecture about free divisors
• On strong Euler-homogeneity and Saito-holonomicity for complex hypersurfaces

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