Local dimension of differential algebraic variety

TL;DR

This paper explores the relationship between local and global dimensions of differential algebraic varieties, proving tangent space dimensions match the variety's dimension and classifying tangent spaces in specific cases.

Contribution

It establishes that tangent space dimensions at regular points equal the variety's dimension and provides a classification for tangent spaces with one derivation.

Findings

Tangent space dimension equals the variety's dimension at regular points.

Classification of tangent spaces in the case of one derivation.

Proof of the equivalence between local and global characteristics.

Abstract

We consider a relation between local and global characteristics of a differential algebraic variety. We prove that dimension of tangent space for every regular point of an irreducible differential algebraic variety coincides with dimension of the variety. Additionally, we classify tangent spaces at regular points in the case of one derivation.