Lifting Lagrangian immersions in $\mathbb{C}{P}^{n-1}$ to Lagrangian cones in ${\mathbb{C}}^n$

Abstract

In this paper we show how to lift Lagrangian immersions in $\mathbb{C}{P}^{n-1}$ to produce Lagrangian cones in ${\mathbb{C}}^n$, and use this process to produce several families of examples of Lagrangian cones and special Lagrangian cones. Moreover we show how to produce Lagrangian cones, isotopic to the Harvey-Lawson and trivial cones, whose projections to $\mathbb{C}{P}^{n-1}$ are immersions with few transverse double points.

28 Pages, 7 figures