2017
DOI: 10.1007/s12220-017-9942-9
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K-Semistability of cscK Manifolds with Transcendental Cohomology Class

Abstract: We prove that constant scalar curvature Kähler (cscK) manifolds with transcendental cohomology class are K-semistable, naturally generalising the situation for polarised manifolds. Relying on a recent result by R. Berman, T. Darvas and C. Lu regarding properness of the K-energy, it moreover follows that cscK manifolds with discrete automorphism group are uniformly K-stable. As a main step of the proof we establish, in the general Kähler setting, a formula relating the (generalised) Donaldson–Futaki invariant t… Show more

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Cited by 29 publications
(54 citation statements)
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“…Donaldson also asked whether the above result holds for general Hölder conjugate pairs ( p, q); this answers his question. When (X, [ω]) admits a cscK metric, this implies (X, [ω]) is K-semistable, giving a slightly different proof of the main results of [24,43]. However, the main interest in Theorem 1.4 is in the case that (X, [ω]) does not admit a cscK metric.…”
Section: Here T Denotes the Set Of Test Configurations For (X [ω]) mentioning
confidence: 99%
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“…Donaldson also asked whether the above result holds for general Hölder conjugate pairs ( p, q); this answers his question. When (X, [ω]) admits a cscK metric, this implies (X, [ω]) is K-semistable, giving a slightly different proof of the main results of [24,43]. However, the main interest in Theorem 1.4 is in the case that (X, [ω]) does not admit a cscK metric.…”
Section: Here T Denotes the Set Of Test Configurations For (X [ω]) mentioning
confidence: 99%
“…Although this article is essentially a sequel to [24,43], where Theorem 1.1 was proven, the techniques used are very different. In [24,43] the main theme was to differentiate energy functionals on the space of Kähler metrics along certain paths induced by test configurations.…”
Section: Comparison With Other Workmentioning
confidence: 99%
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