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).


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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