# Moduli Spaces of Germs of Semiquasihomogeneous Legendrian Curves

## TL;DR

This paper constructs a moduli space for Legendrian curve singularities, focusing on those that are conormals of plane curves with a single Puiseux pair, using a contact analogue of the Kodaira-Spencer map.

## Contribution

It introduces a new moduli space framework for Legendrian curve singularities, specifically for conormal curves with one Puiseux pair, via a contact Kodaira-Spencer map.

## Key findings

- Established a contact analogue of the Kodaira-Spencer map for Legendrian curves.
- Constructed a moduli space classifying Legendrian curve singularities.
- Focused on conormal curves of plane curves with one Puiseux pair.

## Abstract

We construct a moduli space for Legendrian curves singularities which are contactomorphic-equivalent and equisingular through a contact analogue of the Kodaira-Spencer map for curve singularities. We focus on the specific case of Legendrian curves which are the conormal of a plane curve with one Puiseux pair.