The Relation Type of Varieties

TL;DR

This paper introduces the relation type of analytic and formal algebras, demonstrating its invariance and defining it via Andre9-Quillen homology, with applications to schemes, varieties, and algebroid structures.

Contribution

It defines the relation type for various algebraic structures and proves its invariance using homological methods, extending understanding of algebraic and geometric invariants.

Findings

Relation type is well-defined and invariant.

Relation type can be described using Andre9-Quillen homology.

Invariant for schemes, varieties, and algebroid varieties.

Abstract

In this paper, we introduce the notion of relation type of analytic and formal algebras and prove that it is well-defined and invariant by describing this notion in terms of the Andr\'e-Quillen homology and using the Jacobi-Zariski long exact sequence of homology. In particular, the relation type is an invariant of schemes of finite type over a field, analytic varieties, and algebroid varieties.