Compact moduli of noncommutative projective planes

Abstract

We introduce the notion of the moduli stack of relations of a quiver. When the quiver with relations is derived-equivalent to an algebraic variety, the corresponding compact moduli scheme can be viewed as a compact moduli of noncommutative deformations of the variety. We study the case of noncommutative projective planes in detail, and discuss its relation with geometry of elliptic curves with level 3 structures.

28 pages, 3 figures

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• G-algebras, twistings, and equivalences of graded categories
• The automorphism group of ${\overline{M}}_{g,n}$
• Quantum entanglement, Calabi-Yau manifolds, and noncommutative algebraic geometry
• Automorphisms of path coalgebras and applications

Cited by in corpus (7)

• Deformations of path algebras of quivers with relations
• Quantum Projective Planes Finite over their Centers
• Moduli spaces of Einstein-Hermitian generalized connections over generalized Kahler manifolds of symplectic type
• Noncommutative rigidity of the moduli stack of stable pointed curves
• Matsushima-Lichnerowicz type theorems of Lie algebra of automorphisms of generalized Kähler manifolds of symplectic type
• Moduli of noncommutative Hirzebruch surfaces
• On the stability of regular algebras