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K-semistability of cscK manifolds with transcendental cohomology class. (arXiv:1601.07659v2 [math.DG] UPDATED)
来源于:arXiv
We prove that constant scalar curvature K\"ahler (cscK) manifolds with
transcendental cohomology class are K-semistable, naturally generalising the
situation for polarised manifolds. Relying on a very recent result by R.
Berman, T. Darvas and C. Lu regarding properness of the K-energy, it moreover
follows that cscK manifolds with finite automorphism group are uniformly
K-stable. As a main step of the proof we establish, in the general K\"ahler
setting, a formula relating the (generalised) Donaldson-Futaki invariant to the
asymptotic slope of the K-energy along weak geodesic rays. 查看全文>>