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arXiv · 1601.07659

K-semistability of cscK manifolds with transcendental cohomology class

Zakarias Sjöström Dyrefelt
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Abstract

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.

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Zakarias Sjöström Dyrefelt. 2016-01-28. K-semistability of cscK manifolds with transcendental cohomology class. https://doi.org/10.1007/s12220-017-9942-9

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