Blow-ups and resolutions of strong Kähler with torsion metrics

2008/04/02 by Anna Fino, Fino, Anna, Адриано Томассини +1
Mathematics · Physics and Astronomy · #22E25 #53C15 #58U25 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0804.0397

openalex publication_date 2008/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I
• On the Cohomology of Compact Homogeneous Spaces of Nilpotent Lie Groups

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• On cohomological and formal properties of Strong Kähler with torsion and astheno-Kähler metrics
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