Deformations of Noncompact Complex Curves and Meromorphic Envelopes of Spheres
Complex Variables
2015-06-26 v2 Differential Geometry
Symplectic Geometry
Abstract
We study the envelopes of meromorphy of neighborhoods of symplectically immersed two-spheres in complex K\"ahler surfaces using the Gromov's theory of pseudoholomorphic curves. The construction of a complete family of holomorphic deformations of a non-compact complex curve in a complex manifold, parametrized by a finite codimension analytic subset of a Banach ball, is given. The existence of this family is used to prove a generalization of Levi's continuity principle, which is applied to describe envelopes of meromorphy.
Keywords
Cite
@article{arxiv.math/9812005,
title = {Deformations of Noncompact Complex Curves and Meromorphic Envelopes of Spheres},
author = {S. M. Ivashkovich and V. V. Shevchishin},
journal= {arXiv preprint arXiv:math/9812005},
year = {2015}
}
Comments
36 pages, AMS-TeX, 7 epsf-figures. To be published in "Mathematical Sbornik". Replaced version: some minor TeX corrections