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Title:
Holomorphic Poisson structures and generalized Kähler metrics
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Abstract:
Since the introduction of generalized Kahler geometry in 1984 by Gates, Hull, and Rocek in the context of two-dimensional supersymmetric sigma models, we have lacked a general understanding of the degrees of freedom inherent in the geometry. In particular, the description of a usual Kahler structure in terms of a complex manifold together with a local Kahler potential function is not available for generalized Kahler structures, despite many positive indications in the literature over the last decade. I will explain how holomorphic Poisson geometry may be used to solve this problem and to obtain new constructions of generalized Kahler metrics. This is based on the paper arXiv:1804.05412 [math.DG], joint with Francis Bischoff and Maxim Zabzine.
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