Noncommutative complex geometry of the quantum projective space

Abstract

We define holomorphic structures on canonical line bundles of the quantum projective space $\qp^{\ell}_q$ and identify their space of holomorphic sections. This determines the quantum homogeneous coordinate ring of the quantum projective space. We show that the fundamental class of $\qp^{\ell}_q$ is naturally presented by a twisted positive Hochschild cocycle. Finally, we verify the main statements of Riemann-Roch formula and Serre duality for $\qp^{1}_q$ and $\qp^{2}_q$.

References in corpus (1)

• The Noncommutative Geometry of the Quantum Projective Plane

Cited by in corpus (7)

• Quantum Bundle Description of the Quantum Projective Spaces
• Holomorphic Relative Hopf Modules over the Irreducible Quantum Flag Manifolds
• Dequantization via quantum channels
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• Fubini-Study metrics and Levi-Civita connections on quantum projective spaces
• Twisted sigma-model solitons on the quantum projective line