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A balanced proper modification of \(P_ 3\). (English) Zbl 0761.53034

A proper modification \(M\) of a Kähler manifold is not necessarily Kähler, but there is a conjecture that \(M\) should always be balanced, i.e. there exists a metric on \(M\) such that the trace of the torsion of the Chern connection vanishes. The authors prove: the 3-dimensional Hironaka manifold, constructed from \(\mathbb{C} P^ 3\) by modification, is balanced.

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
32Q99 Complex manifolds
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