Abstract
In noncommutative algebraic geometry, noncommutative quadric hypersurfaces are major objects of study. In this paper, we focus on studying noncommutative conics ProjncA 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 ProjncA up to isomorphism of noncommutative schemes.
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