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We show that the blow-up of a generalized Kähler 4-manifold in a nondegenerate complex point admits a generalized Kähler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a tubular neighbourhood of the exceptional divisor. To accomplish this, we develop a blow-up operation for bi-Hermitian manifolds.
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Dec 3, 2011
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