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arXiv · 1105.0456

Noncommutative complex geometry of the quantum projective space

Masoud Khalkhali·Ali Moatadelro
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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 $\qp^{2}_q$.

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BibTeXRIS

Masoud Khalkhali, Ali Moatadelro. 2011-05-02. Noncommutative complex geometry of the quantum projective space. https://doi.org/10.1016/j.geomphys.2011.08.004

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