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On the Strominger system and holomorphic deformations. (English) Zbl 1444.32012

Let \(X\) be a compact complex manifold with holomorphically trivial canonical bundle. The existence of a “canonical” Hermitian metric on \(X\) is obtained if there exists a solution for the so-called Strominger system. For instance, if \(X\) is Kähler Calabi-Yau, this system has a solution. It is known that there are non-Kähler manifolds which are solutions of the Strominger system [J. Li and S. Yau, J. Differ. Geom. 70, No. 1, 143–181 (2005; Zbl 1102.53052)]. If the Strominger system has solution for \(X\), then this manifold is said to have the Strominger property. (So, by the above, Kähler Calabi-Yau manifolds have the Strominger property). In this paper the authors prove that the Strominger property is not stable, meaning that such a property may be lost under holomorphic deformations.

MSC:

32G05 Deformations of complex structures
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory

Citations:

Zbl 1102.53052
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References:

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