A Geometric Compactification Of The Moduli Stack Of Left Invariant Complex Structures On A Lie Group

TL;DR

This paper introduces a geometric compactification of the moduli stack of left invariant complex structures on Lie groups, incorporating CR structures as boundary points to extend the moduli space.

Contribution

It provides a novel geometric compactification framework for the moduli stack, including boundary points characterized by CR structures transverse to a foliation.

Findings

Constructed a compactification of the moduli stack.

Identified CR structures as boundary points.

Extended the moduli space to include these boundary structures.

Abstract

We describe a geometric compactification of the moduli stack of left invariant complex structures on a fixed real Lie group or a fixed quotient. The extra points are CR structures transverse to a real foliation.