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arXiv · 1803.07611

Compact complex surfaces with no nonconstant meromorphic functions

Raymond O. Wells Jr
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Abstract

In 1949 Siegel gave an example of a complex two-torus with no nonconstant meromorphic functions. In 1964 Kodaira showed that compact complex surfaces with no nonconstant meromorphic must be of the following three types: tori, Hopf type surfaces with first Betti number equal to one, and K3 surfaces. In this paper we show that surfaces of these three types have a dense set of surfaces in their natural moduli spaces with no nonconstant meromorphic functions.

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Raymond O. Wells Jr. 2018-05-22. Compact complex surfaces with no nonconstant meromorphic functions. https://arxiv.org/abs/1803.07611

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