Line bundles defined by the Schwarz function

Björn Gustafsson; Mihai Putinar

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arXiv · 1711.03281

Line bundles defined by the Schwarz function

Björn Gustafsson·Mihai Putinar

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Abstract

Cauchy and exponential transforms are characterized, and constructed, as canonical holomorphic sections of certain line bundles on the Riemann sphere defined in terms of the Schwarz function. A well known natural connection between Schwarz reflection and line bundles defined on the Schottky double of a planar domain is briefly discussed in the same context.

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Björn Gustafsson, Mihai Putinar. 2017-11-09. Line bundles defined by the Schwarz function. https://arxiv.org/abs/1711.03281

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