Abstract
We study blow-ups in generalized Kähler geometry. The natural candidates for submanifolds to be blown-up are those which are generalized Poisson submanifolds for one of the two generalized complex structures and can be blown up in a generalized complex manner. We show that the bi-Hermitian structure underlying the generalized Kähler pair lifts to a degenerate bi-Hermitian structure on this blow-up. Then, using a deformation procedure based on potentials in Kähler geometry, we identify two concrete situations in which one can deform the degenerate structure on the blow-up into a non-degenerate one. We end with a study of generalized Kähler Lie groups and give a concrete example on \({(S^1)^n \times (S^3)^m}\), for n + m even.
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Communicated by N. Nekrasov
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van der Leer Durán, J.L. Blow-Ups in Generalized Kähler Geometry. Commun. Math. Phys. 357, 1133–1156 (2018). https://doi.org/10.1007/s00220-017-3039-y
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DOI: https://doi.org/10.1007/s00220-017-3039-y