Pseudo-holomorphic curves and envelopes of meromorphy of two-spheres in $CP^2$

Details Pseudo-holomorphic curves and envelopes of meromorphy of two-spheres in $CP^2$ Pseudo-holomorphic curves and envelopes of meromorphy of two-spheres in $CP^2$

1998-04-03

arxiv.org/abs/math/9804014v1

Mathematics

Complex Variables

Scientific paper

We prove that the envelope of meromorphy of any imbedded symplectic sphere in $CP^2$ coincides with the whole $CP^2$. 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.

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