scholarly journals HOLOMORPHIC QUILLEN DETERMINANT LINE BUNDLES ON INTEGRAL COMPACT KAHLER MANIFOLDS

2013 ◽  
Vol 64 (3) ◽  
pp. 785-794 ◽  
Author(s):  
R. Dey ◽  
V. Mathai
Keyword(s):  
Kähler Manifolds ◽  
Line Bundles ◽  
Kahler Manifolds ◽  
Determinant Line Bundles ◽  
Quillen Determinant

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 PSEUDO-EFFECTIVE LINE BUNDLES ON COMPACT KÄHLER MANIFOLDS

2001 ◽  
Vol 12 (06) ◽  
pp. 689-741 ◽  
Author(s):  
JEAN-PIERRE DEMAILLY ◽  
THOMAS PETERNELL ◽  
MICHAEL SCHNEIDER
Keyword(s):  
Line Bundle ◽  
Vector Bundles ◽  
Kähler Manifolds ◽  
Line Bundles ◽  
Kahler Manifolds ◽  
Ideal Sheaf ◽  
Multiplier Ideal Sheaf ◽  
Albanese Map ◽  
Multiplier Ideal ◽  
Hard Lefschetz Theorem

The goal of this work is to pursue the study of pseudo-effective line bundles and vector bundles. Our first result is a generalization of the Hard Lefschetz theorem for cohomology with values in a pseudo-effective line bundle. The Lefschetz map is shown to be surjective when (and, in general, only when) the pseudo-effective line bundle is twisted by its multiplier ideal sheaf. This result has several geometric applications, e.g. to the study of compact Kähler manifolds with pseudo-effective canonical or anti-canonical line bundles. Another concern is to understand pseudo-effectivity in more algebraic terms. In this direction, we introduce the concept of an "almost" nef line bundle, and mean by this that the degree of the bundle is nonnegative on sufficiently generic curves. It can be shown that pseudo-effective line bundles are almost nef, and our hope is that the converse also holds true. This can be checked in some cases, e.g. for the canonical bundle of a projective 3-fold. From this, we derive some geometric properties of the Albanese map of compact Kähler 3-folds.

Sunada transplantation and isogeny of intermediate Jacobians of compact Kähler manifolds

2020 ◽  
Vol 72 (1) ◽  
pp. 127-147
Author(s):  
Carolyn Gordon ◽  
Eran Makover ◽  
Bjoern Muetzel ◽  
David Webb
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

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