Minimal Lagrangian 2-tori in CP^2 come in real families of every dimension

TL;DR

This paper demonstrates that minimal Lagrangian 2-tori in complex projective space form real families of all dimensions, using integrable systems and spectral curve methods to describe their structure.

Contribution

It establishes the existence of real n-dimensional families of minimal Lagrangian tori in CP^2 for all non-negative integers n, linking them to integrable systems and spectral data.

Findings

Existence of n-dimensional families of minimal Lagrangian tori in CP^2 for all n

Connection between these tori and integrable systems via spectral curve data

Construction of special Lagrangian cones in C^3 with torus links

Abstract

We show that for every non-negative integer n there is a real n-dimensional family of minimal Lagrangian tori in CP^2, and hence of special Lagrangian cones in C^3 whose link is a torus. The proof utilises the fact that such tori arise from integrable systems, and can be described using algebro-geometric (spectral curve) data.