1996/04/16 by Stefano Trapani, Trapani, Stefano
Mathematics · #32 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:32
paper · pdf · doi:10.48550/arxiv.math/9604202
arxiv created 1996/04/16 · openalex publication_date 1996/04/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let S be a generic submanifold of CN of real codimension m. In this work we continue the study, carried over by various authors, of the set of analytic discs attached to S. Let M be the set of analytic discs attached to S. Given q ∈ S let Mq be the set of discs ϕ in M such that ϕ_(1). B. Trepreau and other authors gave sufficient conditions for M to be a manifold in a neighborhood of a given disc. We give conditions for Mq to be a manifold. When this conditions are satisfied we look at the map on M given by ϕ→ ϕ(0), and we describe the image of its differential, (in particular we determine its dimension). We then do the same for the map ϕ→ ϕ(-1) on Mq. For example we find as a corollary that if S has only minimal points, then there exists an open dense subset Omega in M such that the restriction of the map ϕ→ ϕ(0) to Ω is an open map with value in CN.