Local polynomial convexity of the unfolded Whitney umbrella in $\mathbb C^2$

TL;DR

This paper proves that most Lagrangian surfaces with Whitney umbrella singularities in complex two-space are locally polynomially convex near those singularities, enhancing understanding of their local geometric structure.

Contribution

It establishes the generic local polynomial convexity of Lagrangian surfaces with Whitney umbrella singularities in ^2, a new result in complex geometry and symplectic topology.

Findings

Most such surfaces are locally polynomially convex near the singularity

The result applies generically to Lagrangian surfaces with Whitney umbrella singularities

Provides new insights into the local structure of singular Lagrangian surfaces

Abstract

The paper considers a class of Lagrangian surfaces in $\mathbb C^2$ 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.