Noncommutative conics in Calabi-Yau quantum projective planes

Abstract

In noncommutative algebraic geometry, noncommutative quadric hypersurfaces are major objects of study. In this paper, we focus on studying noncommutative conics $\mathrm{Pro}{\mathrm{j}}_{\mathrm{nc}}A$ 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 $\mathrm{Pro}{\mathrm{j}}_{\mathrm{nc}}A$ up to isomorphism of noncommutative schemes.

arXiv comment28 pages

References in corpus (8)

• Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities
• Noncommutative Knörrer's periodicity theorem and noncommutative quadric hypersurfaces
• AS-regularity of geometric algebras of plane cubic curves
• Clifford deformations of Koszul Frobenius algebras and noncommutative quadrics
• Noncommutative matrix factorizations with an application to skew exterior algebras
• Quantum Projective Planes Finite over their Centers
• Some Interesting Features of Memristor CNN
• Derived categories of skew quadric hypersurfaces

Cited by in corpus (1)

• Generalized Knörrer's Periodicity Theorem