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Blow-ups in generalized K\"ahler geometry by Duran, J. L. van der Leer is a scholarly article available to read on EtoBox.

What is Blow-ups in generalized K\"ahler geometry about?

We continue the study of blow-ups in generalized complex geometry with the blow-up theory for generalized K\"ahler manifolds. The natural candidates for submanifolds to be blown-up are those which are generalized Poisson 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 K\"ahler pair lifts to a degenerate bi-Hermitian structure on this blow-up. Then, using a deformation procedure based on potentials in K\"ahler 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 an investigation of generalized K\"ahler Lie groups and give a concrete example on $(S^1)^n\times (S^3)^m$, for $n+m$ even.

Author

Duran, J. L. van der Leer

Published

2016

Language

EN