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Tower of Coverings and Complex Structures on Four Dimensional Manifolds
by Sai-Kee Yeung

Vol. 8 No. 2 (2013) P.269~P.283

ABSTRACT

We study a tower of coverings of a real four dimensional manifold and its relations to properties such as complex structures and existence of meromorphic functions. This allows us revisit the question of existence of a complex structure on an almost complex surface from a perspective different from the usual one. A consequence is the existence of an almost complex surface with any prescribed set of Chern numbers $c_1^2$ and $c_2$ satisfying the Noether relation but supporting no integrable 'almost' complex structure.

KEYWORDS
almost complex structure, complex structure, projective algebraicity

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 32Q55, 32Q60, 53C15, 14J99

MILESTONES