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Journal of Differential Geometry 58 (2001), 331-370.

Uniqueness of symplectic canonical class, surface cone and symplectic cone of 4-manifolds with b+=1

Tian-Jun Li & Ai-Ko Liu

Abstract:

Let $M$ be a closed oriented smooth $4$-manifold admitting symplectic structures. If $M$ is minimal and has $b^+=1$, we prove that there is a unique symplectic canonical class up to sign, and any real second cohomology class of positive square is represented by symplectic forms. Similar results hold when $M$ is not minimal.