Geodesic
A Complete Classification of 3-dimensional Quadratic AS-regular Algebras of Type EC
Canadian mathematical bulletin, Tome 64 (2021) no. 1, pp. 123-141

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DOI

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.
DOI : 10.4153/S0008439520000302
Mots-clés : AS-regular algebras, geometric algebras, Calabi-Yau algebras, superpotentials, elliptic curves 
Matsuno, Masaki. A Complete Classification of 3-dimensional Quadratic AS-regular Algebras of Type EC. Canadian mathematical bulletin, Tome 64 (2021) no. 1, pp. 123-141. doi: 10.4153/S0008439520000302
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     year = {2021},
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