Article contents
A Complete Classification of 3-dimensional Quadratic AS-regular Algebras of Type EC
Published online by Cambridge University Press: 27 April 2020
Abstract
Classification of AS-regular algebras is one of the main interests in noncommutative algebraic geometry. We say that a $3$-dimensional quadratic AS-regular algebra is of Type EC if its point scheme is an elliptic curve in $\mathbb {P}^{2}$. In this paper, we give a complete list of geometric pairs and a complete list of twisted superpotentials corresponding to such algebras. As an application, we show that there are only two exceptions up to isomorphism among all $3$-dimensional quadratic AS-regular algebras that cannot be written as a twist of a Calabi–Yau AS-regular algebra by a graded algebra automorphism.
- Type
- Article
- Information
- Copyright
- © Canadian Mathematical Society 2020
References
- 6
- Cited by