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Given a smooth, closed, oriented 4-manifold X and alpha in H_2(X,Z) such thatalpha.alpha > 0, a closed 2-form w is constructed, Poincare dual to alpha,which is symplectic on the complement of a finite set of unknotted circles. Thenumber of circles, counted with sign, is given by d = (c_1(s)^2 -3sigma(X)-2chi(X))/4, where s is a certain spin^C structure naturally associated to w.

Constructing symplectic forms on 4–manifolds which vanish on circles