scholarly journals Equidistribution results for singular metrics on line bundles

2015 ◽  
Vol 48 (3) ◽  
pp. 497-536 ◽  
Author(s):  
Dan Coman ◽  
George Marinescu
Keyword(s):  
Line Bundles ◽  
Singular Metrics ◽  
On Line

Some Results on Line Bundles over Susy-Curves

1990 ◽  
pp. 675-680
Author(s):  
C. Bartocci ◽  
U. Bruzzo ◽  
D. Hernández Ruipérez
Keyword(s):  
Line Bundles ◽  
On Line

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 Positivity properties of metrics and delta-forms

2019 ◽  
Vol 2019 (752) ◽  
pp. 141-177 ◽  
Author(s):  
Walter Gubler ◽  
Klaus Künnemann
Keyword(s):  
Algebraic Variety ◽  
Abelian Varieties ◽  
Toric Varieties ◽  
Convex Geometry ◽  
Piecewise Smooth ◽  
Line Bundles ◽  
Canonical Metrics ◽  
On Line

Abstract In previous work, we have introduced δ-forms on the Berkovich analytification of an algebraic variety in order to study smooth or formal metrics via their associated Chern δ-forms. In this paper, we investigate positivity properties of δ-forms and δ-currents. This leads to various plurisubharmonicity notions for continuous metrics on line bundles. In the case of a formal metric, we show that many of these positivity notions are equivalent to Zhang’s semipositivity. For piecewise smooth metrics, we prove that plurisubharmonicity can be tested on tropical charts in terms of convex geometry. We apply this to smooth metrics, to canonical metrics on abelian varieties and to toric metrics on toric varieties.

scholarly journals Lefschetz–Bott Fibrations on Line Bundles Over Symplectic Manifolds

2020 ◽  
Author(s):  
Takahiro Oba
Keyword(s):  
Unit Disk ◽  
Blow Up ◽  
Contact Manifold ◽  
Symplectic Manifolds ◽  
Line Bundles ◽  
Complex Line ◽  
Open Book ◽  
Type Singularity ◽  
On Line ◽  
Symplectic Filling

Abstract We describe Lefschetz–Bott fibrations on complex line bundles over symplectic manifolds explicitly. As an application, we show that the link of the $A_{k}$-type singularity has more than one strong symplectic filling up to homotopy and blow-up at points when the dimension of the link is greater than or equal to $5$. In the appendix, we show that the total space of a Lefschetz–Bott fibration over the unit disk serves as a strong symplectic filling of a contact manifold compatible with an open book induced by the fibration.

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