Symplectic surfaces and generic J-holomorphic structures on 4-manifolds
Abstract
Description
It is a well known fact that every embedded symplectic surface $Σ$ in a symplectic 4-manifold $(X^4,ω)$ can be made $J$-holomorphic for some almost-complex structure $J$ compatible with $ω$. 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.
Minor changes were made upon referee's suggestion. Updated references. To be published in Illinois J. Math
Minor changes were made upon referee's suggestion. Updated references. To be published in Illinois J. Math