Symplectic surfaces and generic J-holomorphic structures on 4-manifolds

Details Symplectic surfaces and generic J-holomorphic structures on 4-manifolds Symplectic surfaces and generic J-holomorphic structures on 4-manifolds

2002-07-04

arxiv.org/abs/math/0207052v2

Mathematics

Symplectic Geometry

Minor changes were made upon referee's suggestion. Updated references. To be published in Illinois J. Math

Scientific paper

It is a well known fact that every embedded symplectic surface $\Sigma$ in a symplectic 4-manifold $(X^4,\omega)$ can be made $J$-holomorphic for some almost-complex structure $J$ compatible with $\omega$. In this paper we investigate when such a $J$ can be chosen from a generic set of almost-complex structures. As an application we give examples of smooth and non-empty Seiberg-Witten and Gromov-Witten moduli spaces whose associated invariants are zero.

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