scholarly journals Non-integrated defect relation for meromorphic maps from a Kähler manifold intersecting hypersurfaces in subgeneral ofPn(C)

2017 ◽  
Vol 452 (2) ◽  
pp. 1434-1452 ◽  
Author(s):  
Si Duc Quang ◽  
Nguyen Thi Quynh Phuong ◽  
Nguyen Thi Nhung
Keyword(s):  
Kähler Manifold ◽  
Defect Relation ◽  
Kahler Manifold ◽  
Meromorphic Maps

scholarly journals ON THE DYNAMICAL DEGREES OF MEROMORPHIC MAPS PRESERVING A FIBRATION

2012 ◽  
Vol 14 (06) ◽  
pp. 1250042 ◽  
Author(s):  
TIEN-CUONG DINH ◽  
VIÊT-ANH NGUYÊN ◽  
TUYEN TRUNG TRUONG
Keyword(s):  
Dynamical System ◽  
Kähler Manifold ◽  
Kahler Manifold ◽  
Meromorphic Maps ◽  
Dynamical Degrees ◽  
Compact Kähler Manifold

Let f be a dominant meromorphic self-map on a compact Kähler manifold X which preserves a meromorphic fibration π : X → Y of X over a compact Kähler manifold Y. We compute the dynamical degrees of f in terms of its dynamical degrees relative to the fibration and the dynamical degrees of the map g : Y → Y induced by f. We derive from this result new properties of some fibrations intrinsically associated to X when this manifold admits an interesting dynamical system.

scholarly journals Relative non-pluripolar product of currents

2021 ◽  
Author(s):  
Duc-Viet Vu
Keyword(s):  
Kähler Manifold ◽  
Monotonicity Property ◽  
Necessary Condition ◽  
Positive Current ◽  
Lelong Numbers ◽  
Kahler Manifold ◽  
Closed Positive Current ◽  
Positive Currents ◽  
Compact Kähler Manifold

AbstractLet X be a compact Kähler manifold. Let $$T_1, \ldots , T_m$$ T 1 , … , T m be closed positive currents of bi-degree (1, 1) on X and T an arbitrary closed positive current on X. We introduce the non-pluripolar product relative to T of $$T_1, \ldots , T_m$$ T 1 , … , T m . We recover the well-known non-pluripolar product of $$T_1, \ldots , T_m$$ T 1 , … , T m when T is the current of integration along X. Our main results are a monotonicity property of relative non-pluripolar products, a necessary condition for currents to be of relative full mass intersection in terms of Lelong numbers, and the convexity of weighted classes of currents of relative full mass intersection. The former two results are new even when T is the current of integration along X.

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.

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