A moduli scheme of embedded curve singularities

TL;DR

This paper establishes the existence of a moduli space that parametrizes embedded curve singularities with a fixed Hilbert polynomial, and explores its fundamental properties.

Contribution

It proves the existence of a moduli scheme for embedded curve singularities with specified Hilbert polynomial and investigates its basic characteristics.

Findings

Existence of the moduli scheme for embedded curve singularities.

Basic properties of the moduli space are analyzed.

Provides a foundational framework for studying embedded curve singularities.

Abstract

The main purpose of this paper is to prove the existence of the moduli space parameterizing the embedded curve singularities of $(k^N,0)$ with an admissible Hilbert polynomial and to study its basic properties.