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Blow-ups and resolutions of strong K\"ahler with torsion metrics
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On a compact complex manifold we study the behaviour of strong K\"ahler with torsion (strong KT) structures under small deformations of the complex structure and the problem of extension of a strong KT metric. In this context we obtain the analogous result of Miyaoka extension theorem. Studying the blow-up of a strong KT manifold at a point or along a complex submanifold, we prove that a complex orbifold endowed with a strong KT metric admits a strong KT resolution. In this way we obtain new examples of compact simply-connected strong KT manifolds.
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Geometry and symmetries of Hermitian-Einstein and instanton connection moduli spaces
Holomorphic, torsion-parallel vector fields on KT manifolds induce Killing and holomorphic vector fields on Hermitian-Einstein moduli spaces, which become toric or QKT fibrations under extra closure conditions.
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