Deformations of Noncompact Complex Curves and Meromorphic Envelopes of Spheres

Abstract

We study the envelopes of meromorphy of neighborhoods of symplectically immersed two-spheres in complex Kähler 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.

36 pages, AMS-TeX, 7 epsf-figures. To be published in "Mathematical Sbornik". Replaced version: some minor TeX corrections

References in corpus (1)

• Pseudo-holomorphic curves and envelopes of meromorphy of two-spheres in $C{P}^2$

Cited by in corpus (4)

• Complex Curves in Almost-Complex Manifolds and Meromorphic Hulls
• Envelopes of holomorphy and holomorphic discs
• Weak normality of families of meromorphic mappings and bubbling in higher dimensions
• Vanishing Cycles in Holomorphic Foliations by Curves and Foliated Shells