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On a compact complex manifold we study the behaviour of strong K\"ahler withtorsion (strong KT) structures under small deformations of the complexstructure and the problem of extension of a strong KT metric. In this contextwe obtain the analogous result of Miyaoka extension theorem. Studying theblow-up of a strong KT manifold at a point or along a complex submanifold, weprove that a complex orbifold endowed with a strong KT metric admits a strongKT resolution. In this way we obtain new examples of compact simply-connectedstrong KT manifolds.

Blow-ups and resolutions of strong K\"ahler with torsion metrics