Noncommutative conics in Calabi-Yau quantum projective planes

TL;DR

This paper classifies noncommutative conics embedded in Calabi-Yau quantum projective planes, providing a comprehensive understanding of their algebraic structures and scheme isomorphisms in noncommutative algebraic geometry.

Contribution

It offers a complete classification of homogeneous coordinate algebras and noncommutative conics up to isomorphism, advancing the understanding of noncommutative conics in Calabi-Yau quantum planes.

Findings

Complete classification of homogeneous coordinate algebras A

Classification of noncommutative conics up to scheme isomorphism

Advancement in noncommutative algebraic geometry

Abstract

In noncommutative algebraic geometry, noncommutative quadric hypersurfaces are major objects of study. In this paper, we focus on studying noncommutative conics $\operatorname{Proj_{nc}} A$ embedded into Calabi-Yau quantum projective planes. In particular, we give complete classifications of homogeneous coordinate algebras $A$ of noncommutative conics up to isomorphism of graded algebras, and of noncommutive conics $\operatorname{Proj_{nc}} A$ up to isomorphism of noncommutative schemes.