Jordan-Hölder decomposition of regular (a, b)-modules

2011/04/07 by Piotr P. Karwasz, Karwasz, Piotr P.
Mathematics · #32S25 #32S40 #32S50 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32S25 #msc:32S40 #msc:32S50

paper · pdf · doi:10.48550/arxiv.1104.1246

10 pages

openalex publication_date 2011/04/07 · arxiv created 2014/12/21 · arxiv updated 2014/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A classical result of singularity theory states that the spectrum of an isolated hypersurface singularity is symmetric with respect to n/2, where n is the dimension of the enclosing space. We prove a similar result for the Jordan-Hölder composition series of the (a,b)-module associated to an isolated hypersurface singularity.

Related

• Finite determination of regular (a,b)-modules
• Singular Hilbert modules on Jordan-Kepler varieties
• Bilinear forms in the Jacobian module and binding of N-spectral chains of a hypersurface with an isolated singularity
• A short constructive proof of Jordan's decomposition theorem
• Transfinite normal and composition series of modules