Positive Line Bundles on Arithmetic Surfaces

1992 ◽  
Vol 136 (3) ◽  
pp. 569 ◽  
Author(s):  
Shouwu Zhang
Keyword(s):  
Line Bundles ◽  
Arithmetic Surfaces ◽  
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 (H, C)-groups with positive line bundles

1987 ◽  
Vol 107 ◽  
pp. 1-11 ◽  
Author(s):  
Yukitaka Abe
Keyword(s):  
Holomorphic Function ◽  
Direct Product ◽  
Lie Group ◽  
Line Bundles ◽  
Positive Line

Let G be a connected complex Lie group. Then there exists the smallest closed complex subgroup G0 of G such that G/G0 is a Stein group (Morimoto). Moreover G0 is a connected abelian Lie group and every holomorphic function on G0 is a constant. G0 is called an (H, C)-group or a toroidal group. Every connected complex abelian Lie group is isomorphic to the direct product G0 × Cm × C*n, where G0 is an (H,C)-group.

scholarly journals Positivity notions for holomorphic line bundles over compact Riemann surfaces

1981 ◽  
Vol 23 (1) ◽  
pp. 5-22
Author(s):  
Joshua H. Rabinowitz
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Line Bundles ◽  
Continuous Evolution ◽  
Compact Riemann Surfaces ◽  
Dimension One ◽  
Positive Line ◽  
Holomorphic Line Bundles

Since the early 1950's, when Kodaira “discovered” positive line bundles, the notion of positivity has undergone a continuous evolution. This paper is intended as an introduction to the study of positivity notions. More specifically, I consider the simplest case - line bundles over compact Riemann surfaces - and compare five positivity notions for such bundles. The results obtained are certainly not new; they are, in fact, known in much greater generality. However, by restricting to the dimension one case, I am able to make use of Riemann surface techniques to significantly simplify the proofs. In fact, this article should be easily understood by anyone familiar with the contents of Gunning's Lectures on Riemann surfaces.

Sign in / Sign up

Export Citation Format

Share Document