Compact complex surfaces with no nonconstant meromorphic functions
Complex Variables
2018-05-23 v2
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.
Cite
@article{arxiv.1803.07611,
title = {Compact complex surfaces with no nonconstant meromorphic functions},
author = {Raymond O. Wells},
journal= {arXiv preprint arXiv:1803.07611},
year = {2018}
}