Clifford quadratic complete intersections

TL;DR

This paper introduces Clifford quadratic complete intersections, explores their properties, and establishes a correspondence with commutative quadratic complete intersections, providing a classification in three variables based on characteristic varieties.

Contribution

It defines Clifford quadratic complete intersections and shows their correspondence with commutative counterparts, offering a classification in three variables.

Findings

Established a one-to-one correspondence with commutative quadratic complete intersections.

Provided a classification of Clifford quadratic complete intersections in three variables.

Analyzed properties of Clifford quantum polynomial algebras.

Abstract

In this paper, we define and study Clifford quadratic complete intersections. After showing some properties of Clifford quantum polynomial algebras, we show that there is a natural one-to-one correspondence between Clifford quadratic complete intersections and commutative quadratic complete intersections. As an application, we give a classification of Clifford quadratic complete intersections in three variables in terms of their characteristic varieties.