Line bundle convexity of pseudoconvex domains in complex manifolds

1991 ◽  
Vol 206 (1) ◽  
pp. 605-615 ◽  
Author(s):  
Karen R. Pinney
Keyword(s):  
Line Bundle ◽  
Pseudoconvex Domains ◽  
Complex Manifolds

Strongly pseudoconvex domains as subvarieties of complex manifolds

2010 ◽  
Vol 132 (2) ◽  
pp. 331-360 ◽  
Author(s):  
Barbara Drinovec Drnovšek ◽  
Franc Forstnerič
Keyword(s):  
Pseudoconvex Domains ◽  
Complex Manifolds ◽  
Strongly Pseudoconvex Domains

The L2 ∂¯-Cauchy problem on pseudoconvex domains and applications

2018 ◽  
Vol 11 (02) ◽  
pp. 1850025
Author(s):  
Sayed Saber
Keyword(s):  
Cauchy Problem ◽  
Positive Integer ◽  
Line Bundle ◽  
Tensor Product ◽  
Smooth Boundary ◽  
Pseudoconvex Domains ◽  
Holomorphic Line Bundle ◽  
Dimension Formula ◽  
Weakly Pseudoconvex Domain ◽  
Support Conditions

Let [Formula: see text] be a complex manifold of dimension [Formula: see text] and [Formula: see text] be a weakly pseudoconvex domain with smooth boundary in [Formula: see text]. Let [Formula: see text] be a holomorphic line bundle over [Formula: see text] which is positive on a neighborhood of [Formula: see text]. Let [Formula: see text] be the [Formula: see text]-times tensor product of [Formula: see text] for positive integer [Formula: see text]. The purpose of this paper is to study the [Formula: see text]-problem with support conditions in [Formula: see text] for forms of type [Formula: see text], [Formula: see text] with values in [Formula: see text]. Applications to the [Formula: see text]-problem for smooth forms on boundaries of [Formula: see text] are given.

Complex manifolds polarized by an ample and spanned line bundle of sectional genus three

1998 ◽  
Vol 71 (2) ◽  
pp. 159-168 ◽  
Author(s):  
Yoshiaki Fukuma ◽  
Hironobu Ishihara
Keyword(s):  
Line Bundle ◽  
Complex Manifolds ◽  
Sectional Genus

scholarly journals The Local Structure of Generalized Contact Bundles

2019 ◽  
Vol 2020 (20) ◽  
pp. 6871-6925 ◽  
Author(s):  
Jonas Schnitzer ◽  
Luca Vitagliano
Keyword(s):  
Line Bundle ◽  
Symplectic Manifold ◽  
Complex Manifold ◽  
Local Structure ◽  
Complex Structure ◽  
Regular Point ◽  
Poisson Geometry ◽  
Splitting Theorem ◽  
Complex Manifolds ◽  
Generalized Complex

Abstract Generalized contact bundles are odd-dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local splitting theorem similar to those appearing in Poisson geometry. In particular, in a neighborhood of a regular point, a generalized contact bundle is either the product of a contact and a complex manifold or the product of a symplectic manifold and a manifold equipped with an integrable complex structure on the gauge algebroid of the trivial line bundle.

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