scholarly journals A remark on covering of compact Kähler manifolds and applications

2021 ◽  
Vol 73 (1) ◽  
pp. 138-148
Author(s):  
V. V. Hung ◽  
H. N. Quy
Keyword(s):  
Upper Bound ◽  
Kähler Manifold ◽  
Kahler Manifolds ◽  
Hölder Continuous ◽  
Kahler Manifold ◽  
Right Hand ◽  
Regularization Techniques ◽  
The Right ◽  
Compact Kähler Manifold ◽  
Monge Ampere

UDC 517.9 Recently, Kolodziej proved that, on a compact Kähler manifold the solutions to the complex Monge – Ampére equation with the right-hand side in are Hölder continuous with the exponent depending on and (see [Math. Ann., <strong>342</strong>, 379-386 (2008)]).Then, by the regularization techniques in[J. Algebraic Geom., <strong>1</strong>, 361-409 (1992)], the authors in [J. Eur. Math. Soc., <strong>16</strong>, 619-647 (2014)] have found the optimal exponent of the solutions.In this paper, we construct a cover of the compact Kähler manifold which only depends on curvature of Then, as an application, base on the arguments in[Math. Ann., <strong>342</strong>, 379-386 (2008)], we show that the solutions are Hölder continuous with the exponent just depending on the function in the right-hand side and upper bound of curvature of  

A POSITIVITY PROPERTY FOR FOLIATIONS ON COMPACT KÄHLER MANIFOLDS

2006 ◽  
Vol 17 (01) ◽  
pp. 35-43 ◽  
Author(s):  
MARCO BRUNELLA
Keyword(s):  
Kähler Manifold ◽  
Rational Curves ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Canonical Bundle ◽  
Positivity Property ◽  
Kahler Manifold ◽  
Compact Kähler Manifold

We prove that the canonical bundle of a foliation by curves on a compact Kähler manifold is pseudoeffective, unless the foliation is a (special) foliation by rational curves.

scholarly journals Zeros of Holomorphic One-Forms and Topology of Kähler Manifolds

2020 ◽  
Author(s):  
Stefan Schreieder
Keyword(s):  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Joint Paper ◽  
And Topology ◽  
Kahler Manifold ◽  
Compact Kähler Manifold

Abstract A conjecture of Kotschick predicts that a compact Kähler manifold $X$ fibres smoothly over the circle if and only if it admits a holomorphic one-form without zeros. In this paper we develop an approach to this conjecture and verify it in dimension two. In a joint paper with Hao [ 10], we use our approach to prove Kotschick’s conjecture for smooth projective three-folds.

scholarly journals Numerical dimension and a Kawamata–Viehweg–Nadel-type vanishing theorem on compact Kähler manifolds

2014 ◽  
Vol 150 (11) ◽  
pp. 1869-1902 ◽  
Author(s):  
Junyan Cao
Keyword(s):  
Line Bundle ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Line Bundles ◽  
Kahler Manifolds ◽  
Vanishing Theorem ◽  
Kahler Manifold ◽  
Singular Metrics ◽  
Compact Kähler Manifold

AbstractLet $X$ be a compact Kähler manifold and let $(L,{\it\varphi})$ be a pseudo-effective line bundle on $X$. We first define a notion of numerical dimension for pseudo-effective line bundles with singular metrics, and then discuss the properties of this numerical dimension. Finally, we prove a very general Kawamata–Viehweg–Nadel-type vanishing theorem on an arbitrary compact Kähler manifold.

scholarly journals The General Definition of the Complex Monge–Ampère Operator on Compact Kähler Manifolds

2010 ◽  
Vol 62 (1) ◽  
pp. 218-239 ◽  
Author(s):  
Yang Xing
Keyword(s):  
Convergence Theorem ◽  
Convex Cone ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
General Definition ◽  
Kahler Manifolds ◽  
Plurisubharmonic Functions ◽  
Definition Of ◽  
Compact Kähler Manifold ◽  
Monge Ampere

AbstractWe introduce a wide subclass of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well defined and the convergence theorem is valid. We also prove that is a convex cone and includes all quasi-plurisubharmonic functions that are in the Cegrell class.

Hölder continuous potentials on manifolds with partially positive curvature

2010 ◽  
Vol 9 (4) ◽  
pp. 705-718 ◽  
Author(s):  
Sławomir Dinew
Keyword(s):  
Positive Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Hölder Continuous ◽  
Bisectional Curvature ◽  
Right Hand ◽  
Monge Ampere

AbstractIt is proved that solutions of the complex Monge–Ampère equation on compact Kähler manifolds with right hand side in Lp, p > 1, are uniformly Hölder continuous under the assumption on non-negative orthogonal bisectional curvature.

scholarly journals Continuous solutions to Monge–Ampère equations on Hermitian manifolds for measures dominated by capacity

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Sławomir Kołodziej ◽  
Ngoc Cuong Nguyen
Keyword(s):  
Hermitian Manifold ◽  
General Measure ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Hermitian Manifolds ◽  
Right Hand ◽  
The Right ◽  
Monge Ampere ◽  
Compact Hermitian Manifold

AbstractWe prove the existence of a continuous quasi-plurisubharmonic solution to the Monge–Ampère equation on a compact Hermitian manifold for a very general measure on the right hand side. We admit measures dominated by capacity in a certain manner, in particular, moderate measures studied by Dinh–Nguyen–Sibony. As a consequence, we give a characterization of measures admitting Hölder continuous quasi-plurisubharmonic potential, inspired by the work of Dinh–Nguyen.

scholarly journals Holomorphic one-forms, fibrations over the circle, and characteristic numbers of Kähler manifolds

2021 ◽  
pp. 1-9
Author(s):  
D. KOTSCHICK
Keyword(s):  
Kähler Manifold ◽  
Analogous Problem ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Smooth Manifolds ◽  
Characteristic Numbers ◽  
Kahler Manifold ◽  
Chern Numbers ◽  
Compact Kähler Manifold

Abstract We prove that the only relation imposed on the Hodge and Chern numbers of a compact Kähler manifold by the existence of a nowhere zero holomorphic one-form is the vanishing of the Hirzebruch genus. We also treat the analogous problem for nowhere zero closed one-forms on smooth manifolds.

scholarly journals An application of a C2-estimate for a complex Monge–Ampère equation

2021 ◽  
pp. 2140007
Author(s):  
Chang Li ◽  
Lei Ni ◽  
Xiaohua Zhu
Keyword(s):  
Line Bundle ◽  
Recent Result ◽  
Kähler Manifold ◽  
Alternate Proof ◽  
Kahler Manifold ◽  
Canonical Line Bundle ◽  
Compact Kähler Manifold ◽  
Monge Ampere

By studying a complex Monge–Ampère equation, we present an alternate proof to a recent result of Chu-Lee-Tam concerning the projectivity of a compact Kähler manifold [Formula: see text] with [Formula: see text] for some integer [Formula: see text] with [Formula: see text], and the ampleness of the canonical line bundle [Formula: see text].

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