scholarly journals Existence of Holomorphic Sections and Perturbation of Positive Line Bundles over q–Concave Manifolds

2016 ◽  
Vol 11 (3) ◽  
Author(s):  
George Marinescu
Keyword(s):  
Line Bundles ◽  
Holomorphic Sections ◽  
Positive Line

scholarly journals A direct approach to Bergman kernel asymptotics for positive line bundles

2008 ◽  
Vol 46 (2) ◽  
pp. 197-217 ◽  
Author(s):  
Robert Berman ◽  
Bo Berndtsson ◽  
Johannes Sjöstrand
Keyword(s):  
Bergman Kernel ◽  
Direct Approach ◽  
Line Bundles ◽  
Bergman Kernel Asymptotics ◽  
Positive Line

scholarly journals Morse inequalities for covering manifolds

2001 ◽  
Vol 163 ◽  
pp. 145-165 ◽  
Author(s):  
Radu Todor ◽  
Ionuţ Chiose ◽  
George Marinescu
Keyword(s):  
Line Bundles ◽  
Invariant Line ◽  
Complex Structures ◽  
Von Neumann ◽  
Holomorphic Sections ◽  
Galois Coverings ◽  
Von Neumann Dimension ◽  
The Stability ◽  
Bounded Below ◽  
Lefschetz Theorems

We study the existence of L2 holomorphic sections of invariant line bundles over Galois coverings. We show that the von Neumann dimension of the space of L2 holomorphic sections is bounded below under weak curvature conditions. We also give criteria for a compact complex space with isolated singularities and some related strongly pseudoconcave manifolds to be Moishezon. As applications we prove the stability of the previous Moishezon pseudoconcave manifolds under perturbation of complex structures as well as weak Lefschetz theorems.

scholarly journals ABELIAN CONFORMAL FIELD THEORY AND DETERMINANT BUNDLES

2007 ◽  
Vol 18 (08) ◽  
pp. 919-993 ◽  
Author(s):  
JØRGEN ELLEGAARD ANDERSEN ◽  
KENJI UENO
Keyword(s):  
Field Theories ◽  
Line Bundles ◽  
Conformal Field Theories ◽  
Nodal Curves ◽  
Conformal Field ◽  
Families Of Curves ◽  
Holomorphic Sections ◽  
Explicit Relation ◽  
Holomorphic Line Bundles ◽  
Determinant Bundles

Following [10], we study a so-called bc-ghost system of zero conformal dimension from the viewpoint of [14, 16]. We show that the ghost vacua construction results in holomorphic line bundles with connections over holomorphic families of curves. We prove that the curvature of these connections are up to a scale the same as the curvature of the connections constructed in [14, 16]. We study the sewing construction for nodal curves and its explicit relation to the constructed connections. Finally we construct preferred holomorphic sections of these line bundles and analyze their behaviour near nodal curves. These results are used in [4] to construct modular functors form the conformal field theories given in [14, 16] by twisting with an appropriate factional power of this Abelian theory.

scholarly journals CONVERGENCE OF FUBINI–STUDY CURRENTS FOR ORBIFOLD LINE BUNDLES

2013 ◽  
Vol 24 (07) ◽  
pp. 1350051 ◽  
Author(s):  
DAN COMAN ◽  
GEORGE MARINESCU
Keyword(s):  
Line Bundle ◽  
Asymptotic Distribution ◽  
Line Bundles ◽  
Singular Line ◽  
Distribution Of Zeros ◽  
Bergman Kernels ◽  
Holomorphic Sections ◽  
Asymptotic Distribution Of Zeros

We discuss positive closed currents and Fubini–Study currents on orbifolds, as well as Bergman kernels of singular Hermitian orbifold line bundles. We prove that the Fubini–Study currents associated to high powers of a semipositive singular line bundle converge weakly to the curvature current on the set where the curvature is strictly positive, generalizing a well-known theorem of Tian. We include applications to the asymptotic distribution of zeros of random holomorphic sections.

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