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An obstruction to semistability of manifolds. (English) Zbl 1058.53056

For a compact connected \(n\)-dimensional Kähler manifold \(M\) with Kähler form sitting in \(2\pi \eta\) for some integral Kähler class \(\eta\), a relevant obstruction due to Futaki and Calabi asserts that if the class \(2\pi \eta\) admits a Kähler metric with constant scalar curvature, then the associated Bando-Calabi-Futaki character vanishes. In this note, the authors announce that the Bando-Calabi-Futaki character is also an obstruction to the semistability in the sense of Tian and to the semistability in the sense of Chow points. The details will appear in: The Bando-Calabi-Futaki character as an obstruction to semistability (Preprint).

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
14L30 Group actions on varieties or schemes (quotients)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
57N65 Algebraic topology of manifolds
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