Twisted cotangent bundles of Hyperkähler manifolds

Fabrizio, Anella,; Höring, Andreas

doi:10.48550/arxiv.1906.11528

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Splittings Of Relative Kähler-einstein Metrics1

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2020

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“…Moreover, the arguments laid out in [AH19,Appendix] show that one can find a sequence t k − → 0 and a closed, positive (1, 1)-current T on X 0 such that F * t k p * t k ω 1 t k converges to T weakly when t k − → 0. Since X 0 is a smooth, compact Kähler manifold, one can write T = γ + dd c v where γ is a smooth, closed (1, 1)-form on X 0 and v ∈ L 1 ( X 0 ).…”

Section: Splittings Of Relative Kähler-einstein Metricsmentioning

confidence: 99%

Algebraic approximation and the decomposition theorem for Kähler Calabi-Yau varieties

Bakker,

Guenancia,

Lehn

2020

Preprint

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We extend the decomposition theorem for numerically K-trivial varieties with log terminal singularities to the Kähler setting. Along the way we prove that all such varieties admit a strong locally trivial algebraic approximation, thus completing the numerically K-trivial case of a conjecture of Campana and Peternell. Contents 1. Introduction 1 2. Locally trivial deformations along foliations and resolutions 4 3. K-trivial varieties and strong approximations 17 4. Reminder on the Douady space 21 5. Splittings of relative tangent sheaves 25 6. Splittings of relative Kähler-Einstein metrics 27 7. Splittings of locally trivial families 34 8. Proof of the decomposition theorem 40 References 41

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Section: Splittings Of Relative Kähler-einstein Metricsmentioning

confidence: 99%