On a compact complex manifold we study the behaviour of strong Kähler 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.
Blow-ups and resolutions of strong Kaehler with torsion metrics / A., Fino; Tomassini, Adriano. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 221:(2009), pp. 914-935. [10.1016/j.aim.2009.02.001]
Blow-ups and resolutions of strong Kaehler with torsion metrics
TOMASSINI, Adriano
2009-01-01
Abstract
On a compact complex manifold we study the behaviour of strong Kähler 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.File | Dimensione | Formato | |
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