2004/02/16 by Jean-François Mattéi, Jean-Francois Mattei, Mattei, Jean-Francois +3 · 3 citations
Mathematics · Physics and Astronomy · #32A10 #32A20 #32B10 #32G34 #32S15 #32S30 #32S45 #32S65 #34C20 #34C35 #58F23 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.CV #math.DS #msc:32A10 #msc:32A20 #msc:32B10 #msc:32G34 #msc:32S15 #msc:32S30 #msc:32S45 #msc:32S65 #msc:34C20 #msc:34C35 #msc:58F23
paper · pdf · doi:10.48550/arxiv.math/0402256
89 pages, french
arxiv created 2004/02/16 · openalex publication_date 2004/02/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a complete list of formal invariants for a large class of formal differential 1-forms \w ∈ \Bbb C [[ x, y]]dx + \Bbb C [[ x, y]]dy. \indent A SL-equisingular deformation is an equireducible deformation which leaves invariant both the local formal types and the holonomy representation of the components of the exceptional divisor. We characterize the 1-forms with finite formal type (t.f.f), i.e. those which admit a semi-universal SL-equisingular deformation, and we give an explicit combinatorial criterion of finiteness. \indent The set of 1-forms with finite formal type contains a dense open set (in the sense of Krull's topology)in the set of 1-forms of the second kind.