Strongly Pseudo-Effective and Numerically Flat Reflexive Sheaves

Wu, Xiaojun

doi:10.1007/s12220-021-00865-0

Cited by 6 publications

(4 citation statements)

References 28 publications

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“…In particular, Theorems 1.2, 1.3 and 1.4 play an important role in the proof. Theorem 1.2, which can be seen as a generalisation of [10], gives a characterisation of numerically flat vector bundles in terms of pseudo-effectivity (see Definition 2.3 for numerically flat vector bundles, and [39] for a generalisation to Kähler manifolds). The proof depends on the theory of admissible Hermitian-Einstein metrics in [7].…”

Section: See Definition 21 and Proposition 22 For Pseudo-effective Ve...mentioning

confidence: 99%

On Projective Manifolds With Pseudo-Effective Tangent Bundle

Hosono¹,

Iwai²,

Matsumura³

2021

J. Inst. Math. Jussieu

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In this paper, we develop the theory of singular Hermitian metrics on vector bundles. As an application, we give a structure theorem of a projective manifold X with pseudo-effective tangent bundle; X admits a smooth fibration $X \to Y$ to a flat projective manifold Y such that its general fibre is rationally connected. Moreover, by applying this structure theorem, we classify all the minimal surfaces with pseudo-effective tangent bundle and study general nonminimal surfaces, which provide examples of (possibly singular) positively curved tangent bundles.

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Section: See Definition 21 and Proposition 22 For Pseudo-effective Ve...mentioning

confidence: 99%

On Projective Manifolds With Pseudo-Effective Tangent Bundle

Hosono¹,

Iwai²,

Matsumura³

2021

J. Inst. Math. Jussieu

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“…where the intersection runs over all closed δω P(E) -positive (1, 1)-currents θ ∈ {ω P(E) } = O P(E) (1) for a Kähler form ω P(E) on P(E), and E + (θ) := {ξ ∈ P(E) : ν(θ, ξ) > 0}. We obtain the following generalization of X. Wu's main result in [Wu22].…”

Section: Introductionmentioning

confidence: 60%

On Lelong Numbers of Generalized Monge-Ampère Products

Sera¹

2022

Preprint

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We consider generalized (mixed) Monge-Ampère products of quasiplurisubharmonic functions (with and without analytic singularities) as they were introduced and studied in several articles written by subsets of M. Andersson, E. Wulcan, Z. B locki, R. Lärkäng, H. Raufi, J. Ruppenthal, and the author. We continue these studies and present estimates for the Lelong numbers of pushforwards of such products by proper holomorphic submersions. Furthermore, we apply these estimates to Chern and Segre currents of pseudoeffective vector bundles. Among other corollaries, we obtain the following generalization of a recent result by X. Wu. If the nonnef locus of a pseudoeffective vector bundle E on a Kähler manifold is contained in a countable union of k-codimensional analytic sets, and if the k-power of the first Chern class of E is trivial, then E is nef.

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“…In Section 4, we study the strongly pseudoeffective (strongly psef for short) orbifold vector bundle over a compact orbifold which generalises the results of [Wu22].…”

Section: Introductionmentioning

confidence: 99%

“…Based on the orbifold version of Demailly's regularisation in Section 3, we can generalise the Serge current techniques in [Wu22] to the orbifold setting.…”

Section: Introductionmentioning

confidence: 99%

On compact Kähler orbifold

Wu¹

2023

Preprint

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In this note, we study compact complex orbifolds. In the first part, we shows the equivalence of two notions of Kähler orbifold. In the second part, we shows various versions of Demailly's regularisation theorems for compact orbifold and study the positivity of orbifold vector bundle. In the last section, we give a version of equivariant GAGA communicated to us by Brion.Proposition A. (Brion) Let X be a projective manifold with an (algebraic) action of a connected reductive group L. Let E be a holomorphic L−equivariant vector bundle over X. Then there exists a connected finite cover L ′ of L such that E is an algebraic L ′ −equivariant vector bundle. This is a generalisation of Theorem 5.2.1 of [Bri18] of rank one case to higher rank case. We also have the following characterisation of projective toric varieties.

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Strongly Pseudo-Effective and Numerically Flat Reflexive Sheaves

Cited by 6 publications

References 28 publications

On Projective Manifolds With Pseudo-Effective Tangent Bundle

On Projective Manifolds With Pseudo-Effective Tangent Bundle

On Lelong Numbers of Generalized Monge-Ampère Products

On compact Kähler orbifold

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