A complete classification of $3$-dimensional quadratic AS-regular algebras of Type EC

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 which cannot be written as a twist of a Calabi-Yau AS-regular algebra by a graded algebra automorphism.

18 pages

References in corpus (2)

• Calabi-Yau algebras
• AS-regularity of geometric algebras of plane cubic curves

Cited by in corpus (1)

• Quantum Projective Planes Finite over their Centers