Moduli spaces of model real submanifolds: two alternative approaches

TL;DR

This paper explores two alternative methods from equivalence theory and Lie symmetries to construct moduli spaces of CR-models, providing new computational approaches and explicitly determining the moduli space M(1,4).

Contribution

It introduces two novel approaches for constructing moduli spaces of CR-models, offering advantages over the invariant theory method and explicitly computes a specific moduli space.

Findings

Two alternative approaches successfully construct moduli spaces.

The moduli space M(1,4) is explicitly computed.

Methods demonstrate advantages over previous invariant theory approaches.

Abstract

Instead of the invariant theory approach employed by Beloshaoka and Mamai for constructing the moduli spaces of Beloshapka's universal CR-models, we consider two alternative approaches borrowed from the theories of equivalence problem and Lie symmetries, each of them having its own advantages. Also the moduli space M(1,4) associated to the class of universal CR-models of CR-dimension 1 and codimension 4 is computed by means of the presented methods.