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Positivity notions for holomorphic line bundles over compact Riemann surfaces

Published online by Cambridge University Press:  17 April 2009

Joshua H. Rabinowitz
Joshua H. Rabinowitz
Affiliation:
Department of Mathematics, University of Illinois at Chicago Circle, Chicago, Illinois 60680, USA.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1981 , pp. 5 - 22
Copyright
Copyright © Australian Mathematical Society 1981

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