Hypercohomologies of truncated twisted holomorphic de Rham complexes

Meng, Lingxu

doi:10.1007/s10455-020-09711-y

Cited by 8 publications

(4 citation statements)

References 12 publications

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“…, which is called the k-th hypercohomology with supports in Φ. Using the results in the earlier version [23] of the present paper, we generalized several classical results for the hypercohomologies of truncated twisted holomorphic de Rham complexes in [25]. Based on the present results, we can extend them to the ones with supports in paracompactifying families.…”

Section: On Column Cohomologies the Inclusionmentioning

confidence: 61%

Blow-up formulae for twisted cohomologies with supports

Meng

2020

Preprint

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We study twisted cohomologies with paracompactifying families of supports. The Künneth theorems, Leray-Hirsch theorems and self-intersection formulae are established. Based on these results, we eventually give explicit expressions of complex blow-up formulae for twisted Dolbeault cohomology on arbitrary complex manifolds and the ones of generalized blow-ups formulae for twisted de Rham cohomology on arbitrary oriented smooth manifolds. These expressions are induced by the morphisms of (simple or double) complexes of spaces of forms and currents rather than just the maps between cohomologies, which help us to obtain the corresponding results for twisted Bott-Chern, Aeppli cohomologies and hypercohomologies of truncated twisted holomorphic de Rham complexes.

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Section: On Column Cohomologies the Inclusionmentioning

confidence: 61%

Blow-up formulae for twisted cohomologies with supports

Meng

2020

Preprint

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“…However, (0.1) is not true for a general compact complex manifold Y . So [1,Theorem 1.2] does not hold.…”

Section: Why [1 Theorem 12] Is Not Truementioning

confidence: 99%

Correction to: Hypercohomologies of truncated twisted holomorphic de Rham complexes

Meng

2023

Ann Glob Anal Geom

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“…Recently, extensive works have been done on the topics of blow-up formulae and the ∂ ∂-lemma. We refer the readers to [6], [7], [14], [42], [28], [29], [30], [31], [32], [51], [53], [47], [23], [22], [34], [38] etc., and the references therein for some resent results.…”

mentioning

confidence: 99%

“…Akin to Proposition B.2, we can establish a projective bundle formula for the truncated holomorphic de Rham cohomology considered in Theorem 3.9. Then the remainder of the proof go through by using the same arguments in the proof of Theorem 3.7; see also [29,Theorem 1.4], [31,Theorem 4.18], or [15,Proposition 8].…”

mentioning

confidence: 99%

Bott-Chern hypercohomology and bimeromorphic invariants

Yang¹,

Yang²

2022

Preprint

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The aim of this article is to study the geometry of Bott-Chern hypercohomology from the bimeromorphic point of view. We construct some new bimeromorphic invariants involving the cohomology for the sheaf of germs of pluriharmonic functions, the truncated holomorphic de Rham cohomology, and the de Rham cohomology. To define these invariants, using a sheaf-theoretic approach, we establish a blow-up formula together with a canonical morphism for the Bott-Chern hypercohomology. In particular, we compute the invariants of some compact complex threefolds, such as Iwasawa manifolds and quintic threefolds.

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Hypercohomologies of truncated twisted holomorphic de Rham complexes

Cited by 8 publications

References 12 publications

Blow-up formulae for twisted cohomologies with supports

Blow-up formulae for twisted cohomologies with supports

Correction to: Hypercohomologies of truncated twisted holomorphic de Rham complexes

Bott-Chern hypercohomology and bimeromorphic invariants

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