Moishezon's conjecture on Moishezon 4-manifolds and symplectic 4-manifolds

A Moishezon 4-manifold is the smooth 4-manifold constructed from a semi-algebraic cuspidal curve in $\mathbb P^2$ and an epimorphism to a symmetric group, with a smooth map to $\mathbb P^2$ that is an unramified covering away from the curve and locally has the behavior of a generic branched morphism. A symplectic 4-manifold is a smooth 4-manifold admitting a closed nondegenerate $2$-form. Moishezon's conjecture. The class of Moishezon 4-manifolds coincides with the class of symplectic 4-manifolds. This proposes that the topological branched-cover construction captures exactly the symplectic smooth 4-manifolds; the supplied source gives no resolution status.