scholarly journals Holomorphic functions of polynomial growth on abelian coverings of a compact complex manifold

1998 ◽  
Vol 6 (3) ◽  
pp. 485-510
Author(s):  
Alexander Brudnyi
Keyword(s):  
Complex Manifold ◽  
Polynomial Growth ◽  
Holomorphic Functions ◽  
Compact Complex Manifold

Remarks on Kähler–Ricci solitons

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Lucio Bedulli ◽  
Anna Gori
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Complex Projective Space ◽  
Ricci Soliton ◽  
Compact Complex Manifold ◽  
Ricci Solitons ◽  
Complex Projective

AbstractWe prove that a compact complex manifold endowed with a Kähler-Ricci soliton cannot be isometrically embedded in a complex projective space ℂℙ

scholarly journals Families of K-3 Surfaces

1972 ◽  
Vol 48 ◽  
pp. 1-17 ◽  
Author(s):  
Alan L. Mayer
Keyword(s):  
Complex Manifold ◽  
Chern Class ◽  
Compact Complex Manifold ◽  
Canonical Sheaf ◽  
First Chern Class

Let V be a 2-dimensional compact complex manifold. V is called a K-3 surface if : a) the irregularity q = dim H1(V, θ) of V vanishes and b) the first Chern class c1 of V vanishes. The canonical sheaf (of holo-morphic 2-forms) K of such a surface is trivial, since q = 0 implies that the Chern class map cx : Pic (V) → H2(V, Z) is injective : thus V has a nowhere zero holomorphic 2-form.

scholarly journals RC-POSITIVITY, VANISHING THEOREMS AND RIGIDITY OF HOLOMORPHIC MAPS

2019 ◽  
pp. 1-16
Author(s):  
Xiaokui Yang
Keyword(s):  
Complex Manifold ◽  
Hermitian Manifold ◽  
Compact Complex Manifold ◽  
Holomorphic Sectional Curvature ◽  
Vanishing Theorems ◽  
Holomorphic Maps ◽  
Holomorphic Map ◽  
Holomorphic Bisectional Curvature ◽  
Tautological Line Bundle ◽  
Compact Complex Manifolds

Let $M$ and $N$ be two compact complex manifolds. We show that if the tautological line bundle ${\mathcal{O}}_{T_{M}^{\ast }}(1)$ is not pseudo-effective and ${\mathcal{O}}_{T_{N}^{\ast }}(1)$ is nef, then there is no non-constant holomorphic map from $M$ to $N$ . In particular, we prove that any holomorphic map from a compact complex manifold $M$ with RC-positive tangent bundle to a compact complex manifold $N$ with nef cotangent bundle must be a constant map. As an application, we obtain that there is no non-constant holomorphic map from a compact Hermitian manifold with positive holomorphic sectional curvature to a Hermitian manifold with non-positive holomorphic bisectional curvature.

Chern-Yamabe problem and Chern-Yamabe soliton

2021 ◽  
Vol 32 (03) ◽  
pp. 2150016
Author(s):  
Pak Tung Ho ◽  
Jinwoo Shin
Keyword(s):  
Scalar Curvature ◽  
Complex Manifold ◽  
The Other ◽  
Compact Complex Manifold ◽  
Yamabe Problem ◽  
Conformal Metric ◽  
Hermitian Metric ◽  
Dimension Formula ◽  
Complex Dimension ◽  
Yamabe Soliton

Let [Formula: see text] be a compact complex manifold of complex dimension [Formula: see text] endowed with a Hermitian metric [Formula: see text]. The Chern-Yamabe problem is to find a conformal metric of [Formula: see text] such that its Chern scalar curvature is constant. In this paper, we prove that the solution to the Chern-Yamabe problem is unique under some conditions. On the other hand, we obtain some results related to the Chern-Yamabe soliton.

On Density Conditions for Interpolation in the Ball

2003 ◽  
Vol 46 (4) ◽  
pp. 559-574 ◽  
Author(s):  
Nicolas Marco ◽  
Xavier Massaneda
Keyword(s):  
Unit Ball ◽  
Polynomial Growth ◽  
Entire Functions ◽  
Holomorphic Functions ◽  
Weighted Bergman Space ◽  
Sufficient Condition ◽  
Density Condition ◽  
Interpolating Sequences ◽  
Class A ◽  
Spaces Of Holomorphic Functions

AbstractIn this paper we study interpolating sequences for two related spaces of holomorphic functions in the unit ball of Cn, n > 1. We first give density conditions for a sequence to be interpolating for the class A−∞ of holomorphic functions with polynomial growth. The sufficient condition is formally identical to the characterizing condition in dimension 1, whereas the necessary one goes along the lines of the results given by Li and Taylor for some spaces of entire functions. In the second part of the paper we show that a density condition, which for n = 1 coincides with the characterizing condition given by Seip, is sufficient for interpolation in the (weighted) Bergman space.

scholarly journals Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms

2020 ◽  
Vol 7 (1) ◽  
pp. 194-214
Author(s):  
Daniele Angella ◽  
Tatsuo Suwa ◽  
Nicoletta Tardini ◽  
Adriano Tomassini
Keyword(s):  
Complex Manifold ◽  
Compact Complex Manifold ◽  
Complex Manifolds ◽  
Dolbeault Cohomology ◽  
Hodge Structures ◽  
Balanced Metric ◽  
The Stability ◽  
Cech Cohomology ◽  
Simply Connected ◽  
Compact Complex Manifolds

AbstractWe construct a simply-connected compact complex non-Kähler manifold satisfying the ∂ ̅∂ -Lemma, and endowed with a balanced metric. To this aim, we were initially aimed at investigating the stability of the property of satisfying the ∂ ̅∂-Lemma under modifications of compact complex manifolds and orbifolds. This question has been recently addressed and answered in [34, 39, 40, 50] with different techniques. Here, we provide a different approach using Čech cohomology theory to study the Dolbeault cohomology of the blowup ̃XZ of a compact complex manifold X along a submanifold Z admitting a holomorphically contractible neighbourhood.

scholarly journals Stable Higgs bundles over positive principal elliptic fibrations

2018 ◽  
Vol 5 (1) ◽  
pp. 195-201
Author(s):  
Indranil Biswas ◽  
Mahan Mj ◽  
Misha Verbitsky
Keyword(s):  
Vector Bundle ◽  
Line Bundle ◽  
Complex Manifold ◽  
Higgs Bundle ◽  
Compact Complex Manifold ◽  
Holomorphic Line Bundle ◽  
Higgs Bundles ◽  
Stable Vector Bundle ◽  
Hermitian Metric ◽  
The Third

AbstractLet M be a compact complex manifold of dimension at least three and Π : M → X a positive principal elliptic fibration, where X is a compact Kähler orbifold. Fix a preferred Hermitian metric on M. In [14], the third author proved that every stable vector bundle on M is of the form L⊕ Π ⃰ B0, where B0 is a stable vector bundle on X, and L is a holomorphic line bundle on M. Here we prove that every stable Higgs bundle on M is of the form (L ⊕ Π ⃰B0, Π ⃰ ɸX), where (B0, ɸX) is a stable Higgs bundle on X and L is a holomorphic line bundle on M.

EXAMPLES OF A NON-VANISHING CONJECTURE OF KAWAMATA

2007 ◽  
Vol 18 (05) ◽  
pp. 527-533
Author(s):  
YU-LIN CHANG
Keyword(s):  
Line Bundle ◽  
Complex Manifold ◽  
Symmetric Spaces ◽  
Sufficient Conditions ◽  
Compact Complex Manifold ◽  
Holomorphic Line Bundle ◽  
Compact Type ◽  
Hermitian Symmetric Spaces ◽  
Canonical Line Bundle ◽  
Positive Holomorphic Line Bundle

Let M be a compact complex manifold with a positive holomorphic line bundle L, and K be its canonical line bundle. We give some sufficient conditions for the non-vanishing of H0(M, K + L). We also show that the criterion can be applied to interesting classes of examples including all compact locally hermitian symmetric spaces of non-compact type, Mostow–Siu [10] surfaces, Kähler threefolds given by Deraux [3] and examples of Zheng [17].

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