Rational convexity of non generic immersed lagrangian submanifolds

TL;DR

This paper proves that immersed Lagrangian submanifolds with quadratic self-tangencies in complex Euclidean space are rationally convex, extending previous results from embedded and transversal cases.

Contribution

It generalizes the concept of rational convexity to include immersed Lagrangian submanifolds with quadratic self-tangencies.

Findings

Immersed Lagrangian submanifolds with quadratic self-tangencies are rationally convex.

Extension of rational convexity results from embedded to certain immersed cases.

Broader understanding of convexity properties in symplectic geometry.

Abstract

We prove that an immersed lagrangian submanifold in $\C^n$ with quadratic self-tangencies is rationally convex. This generalizes former results for the embedded and the immersed transversal cases.