Pseudo-holomorphic curves and envelopes of meromorphy of two-spheres in CP²

1998/04/03 by Sergei Ivashkovich, Ivashkovich, Sergei, Vsevolod Shevchishin +1
Mathematics · #32D10 #58F05 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.CV #math.DG #math.SG #msc:32D10 #msc:58F05

paper · pdf · doi:10.48550/arxiv.math/9804014

arxiv created 1998/04/03 · arxiv updated 2009/11/30

Abstract

We prove that the envelope of meromorphy of any imbedded symplectic sphere in CP² coincides with the whole CP². As a tool for the proof we use the Gromov theory of pseudo-holomorphic curves. Several results in this subject, such as adjunction formula, smoothness of moduli space in the neighborhood of a cusp-curve are improved. We introduce a natural holomorphic structure on the pulled back tangent bundle, in which the differential of a ps.-hol. map in an analytic morphism and describe cusps of ps.-hol. curves using Bennequin index.

Related

• Complex Curves in Almost-Complex Manifolds and Meromorphic Hulls
• Virtual neighborhood technique for pseudo-holomorphic spheres
• A representation for pseudoholomorphic surfaces in spheres
• Pseudoholomoprhic curves on the \mathfrakLCS-fication of contact manifolds
• Some Questions in the Theory of Pseudoholomorphic Curves