Singular hermitian metrics on positive line bundles

1992 ◽  
pp. 87-104 ◽  
Author(s):  
Jean-Pierre Damailly
Keyword(s):  
Line Bundles ◽  
Hermitian Metrics ◽  
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

Topological Invariants and Differential Geometry

2017 ◽  
Author(s):  
Paula Tretkoff
Keyword(s):  
Differential Geometry ◽  
Topological Space ◽  
Chern Class ◽  
Euler Number ◽  
Line Bundles ◽  
Topological Invariants ◽  
Fundamental Groups ◽  
Hermitian Metrics ◽  
Finite Set ◽  
First Chern Class

This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number e(X). The Euler number, also known as the Euler-Poincaré characteristic, is an important invariant of a topological space X. It generalizes the notion of the cardinality of a finite set. The chapter presents the simple formulas for computing the Euler-Poincaré characteristic (Euler number) of many of the spaces to be encountered throughout the book. It also discusses fundamental groups and covering spaces and some basics of the theory of complex manifolds and Hermitian metrics, including the concept of real manifold. Finally, it provides some general facts about divisors, line bundles, and the first Chern class on a complex manifold X.

scholarly journals Distribution of Zeros of Random and Quantum Chaotic Sections of Positive Line Bundles

1999 ◽  
Vol 200 (3) ◽  
pp. 661-683 ◽  
Author(s):  
Bernard Shiffman ◽  
Steve Zelditch
Keyword(s):  
Line Bundles ◽  
Distribution Of Zeros ◽  
Positive Line

scholarly journals Almost complex toric manifolds and positive line bundles

1998 ◽  
Vol 45 (1) ◽  
pp. 95-114
Author(s):  
Akio Hattori
Keyword(s):  
Line Bundles ◽  
Toric Manifolds ◽  
Almost Complex ◽  
Positive Line

Positive Line Bundles on Arithmetic Surfaces

1992 ◽  
Vol 136 (3) ◽  
pp. 569 ◽  
Author(s):  
Shouwu Zhang
Keyword(s):  
Line Bundles ◽  
Arithmetic Surfaces ◽  
Positive Line
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