Lagrangian inclusion with an open Whitney umbrella is rationally convex

TL;DR

This paper proves that certain Lagrangian inclusions of real surfaces with Whitney umbrellas and self-intersections are rationally convex in complex two-space.

Contribution

It establishes the rational convexity of Lagrangian inclusions with Whitney umbrellas and double intersections, extending understanding of complex convexity properties.

Findings

Lagrangian inclusions with Whitney umbrellas are rationally convex.

The result applies to surfaces with double transverse self-intersections.

This advances the theory of rational convexity in complex geometry.

Abstract

It is shown that a Lagrangian inclusion of a real surface in $\mathbb C^2$ with a standard open Whitney umbrella and double transverse self-intersections is rationally convex.