The closure of the symplectic cone of elliptic surfaces
  The symplectic cone of a closed oriented 4-manifold is the set of cohomology classes represented by symplectic forms. A well-known conjecture describes this cone for every minimal Kaehler surface. We consider the case of the elliptic surfaces E(n) and focus on a slightly weaker conjecture for the closure of the symplectic cone. We prove this conjecture in the case of the spin surfaces E(2m) using inflation and the action of self-diffeomorphisms of the elliptic surface. An additional obstruction appears in the non-spin case. 
M. J. D. Hamilton
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