NC deformations of resolved conifold via algebroid stacks
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Abstract
Noncommutative(nc) deformations have been very important to the study of quantum physics and geometric representation theory. In the thesis, we develop a local-to-global approach to study nc geometry. Given a nc crepant resolution A in the sense of Van den Bergh and its nc deformations A^h, we develop a mirror-symmetric method to construct an algebroid stack X^h, and a universal twisted complex which gives a functor between the dg categories of A^h and X^h. We apply this method to the conifold singularity and show that the functor gives a derived equivalence. We also apply the method to K_{P2} and find interesting phenomena occur when h≠0.