Local polynomial convexity of the unfolded Whitney umbrella in \mathbb C²

2011/06/21 by Rasul Shafikov, Shafikov, Rasul, Alexandre Sukhov +1
Mathematics · #32E20 #32E30 #32V40 #53D12 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Symplectic Geometry (math.SG) #math.CV #math.DS #math.SG #msc:32E20 #msc:32E30 #msc:32V40 #msc:53D12

paper · pdf · doi:10.48550/arxiv.1106.4272

26 pages, 7 figures, to appear in IMRN

openalex publication_date 2011/06/21 · arxiv created 2012/08/23 · arxiv updated 2012/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper considers a class of Lagrangian surfaces in \mathbb C² with isolated singularities of the unfolded Whitney umbrella type. We prove that generically such a surface is locally polynomially convex near a singular point of this kind.

Citations

• Polynomially and rationally convex sets

Related

• Lagrangian inclusion with an open Whitney umbrella is rationally convex
• Polynomially convex hulls of singular real manifolds
• Certain real surfaces in ℂ² with isolated singularities
• Certain real surfaces in ℂ² with degenerated CR singularities
• Rational approximation and Lagrangian inclusions