Blow-ups of locally conformally Kahler manifolds

Details Blow-ups of locally conformally Kahler manifolds Blow-ups of locally conformally Kahler manifolds

2011-08-24

arxiv.org/abs/1108.4885v2

Mathematics

Algebraic Geometry

14 pages, ver. 2.0, a couple of lemmas added, some amendmends for dimension 1 subvarieties

Scientific paper

A locally conformally Kahler (LCK) manifold is a manifold which is covered by a Kahler manifold, with the deck transform group acting by homotheties. We show that the blow-up of a compact LCK manifold along a complex submanifold admits an LCK structure if and only if this submanifold is globally conformally Kahler. We also prove that a twistor space (of a compact 4-manifold, a quaternion-Kahler manifold or a Riemannian m anifold) cannot admit an LCK metric, unless it is Kahler.

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