A Kodaira Vanishing Theorem for Noncommutative Kahler Structures
Quantum Algebra
2018-01-26 v2 K-Theory and Homology
Abstract
Using the framework of noncommutative Kahler structures, we generalise to the noncommutative setting the celebrated vanishing theorem of Kodaira for positive line bundles. The result is established under the assumption that the associated Dirac-Dolbeault operator of the line bundle is diagonalisable, an assumption that is shown to always hold in the quantum homogeneous space case. The general theory is then applied to the covariant Kahler structure of the Heckenberger-Kolb calculus of the quantum Grassmannians allowing us to prove a direct q-deformation of the classical Grassmannian Bott-Borel-Weil theorem for positive line bundles.
Cite
@article{arxiv.1801.08125,
title = {A Kodaira Vanishing Theorem for Noncommutative Kahler Structures},
author = {Réamonn Ó Buachalla and Jan Stovicek and Adam-Christiaan van Roosmalen},
journal= {arXiv preprint arXiv:1801.08125},
year = {2018}
}
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54 pages