Uniqueness of Symplectic Canonical Class, Surface Cone and Symplectic Cone of 4-Manifolds with B+ = 1

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.