Dolbeault and Bott-Chern formalities: Deformations and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mo>∂</mml:mo><mml:mover accent="true"><mml:mrow><mml:mo>∂</mml:mo></mml:mrow><mml:mo>‾</mml:mo></mml:mover></mml:math>-lemma

Sferruzza, Tommaso; Томассини, Адриано

doi:10.1016/j.geomphys.2022.104470

Cited by 5 publications

(1 citation statement)

References 23 publications

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“…This approach has been taken e.g. in [ASTT20] and [ST22], see also Appendix A. On the other hand, such a resolution has to be constructed by hand in every specific example and is not guaranteed to exist.Our main technical ingredient is a general resolution procedure with built-in control of the cohomology.…”

Section: Introductionmentioning

confidence: 99%

Frölicher Spectral Sequence and Hodge Structures on the Cohomology of Complex Parallelisable Manifolds

Kasuya

Stelzig

2023

Transformation Groups

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For complex parallelisable manifolds Γ\G, with G a solvable or semisimple complex Lie group, the Frölicher spectral sequence degenerates at the second page. In the solvable case, the de Rham cohomology carries a pure Hodge structure. In contrast, in the semisimple case, purity depends on the lattice, but there is always a direct summand of the de Rham cohomology which does carry a pure Hodge structure and is independent of the lattice.

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Section: Introductionmentioning

confidence: 99%

Frölicher Spectral Sequence and Hodge Structures on the Cohomology of Complex Parallelisable Manifolds

Kasuya

Stelzig

2023

Transformation Groups

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On cohomological and formal properties of strong Kähler with torsion and astheno-Kähler metrics

Sferruzza

Томассини

2023

Math. Z.

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We provide families of compact astheno-Kähler nilmanifolds and we study the behaviour of the complex blowup of such manifolds. We prove that the existence of an astheno-Kähler metric satisfying an extra differential condition is not preserved by blowup. We also study the interplay between Strong Kähler with torsion metrics and geometrically Bott–Chern metrics. We show that Fino–Parton–Salamon nilmanifolds are geometrically-Bott–Chern-formal, whereas we obtain negative results on the product of two copies of primary Kodaira surface, Inoue surface of type$$\mathcal {S}_M$$ S M and on the product of a Kodaira surface with an Inoue surface.

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A Kummer construction for Chern–Ricci flat balanced manifolds

Giusti,

Spotti

2024

Math. Z.

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Given a non-Kähler Calabi–Yau compact orbifold with isolated singularities endowed with a Chern–Ricci flat balanced metric, we study, via a gluing construction, the existence of Chern–Ricci flat balanced metrics on its crepant resolutions, and discuss applications to the search of solutions for the Hull–Strominger system. We also describe the scenario of singular threefolds with ordinary double points, and see that similarly is possible to obtain balanced approximately Chern–Ricci flat metrics.

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Dolbeault and Bott-Chern formalities: Deformations and∂∂‾-lemma

Cited by 5 publications

References 23 publications

Frölicher Spectral Sequence and Hodge Structures on the Cohomology of Complex Parallelisable Manifolds

Frölicher Spectral Sequence and Hodge Structures on the Cohomology of Complex Parallelisable Manifolds

On cohomological and formal properties of strong Kähler with torsion and astheno-Kähler metrics

A Kummer construction for Chern–Ricci flat balanced manifolds

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