# A note on deformations of regular embeddings

## TL;DR

This paper explores the first order deformation space of regular embeddings of reduced algebraic schemes, providing a comparative analysis with existing results by Ran.

## Contribution

It offers a new description of the deformation space and relates it to prior work, enhancing understanding of regular embeddings' deformation theory.

## Key findings

- Provides a detailed description of the first order deformation space.
- Establishes a comparison with Ran's results on deformations.
- Advances the theoretical framework for regular embeddings.

## Abstract

In this paper we give a description of the first order deformation space of a regular embedding of reduced algebraic schemes. We compare our result with results of Ran (in particular [Ran, Prop. 1.3]).