The closure of the symplectic cone of elliptic surfaces

Abstract

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.

arXiv comment12 pages; to appear in J. Symplectic Geom

References in corpus (2)

• The Space of Symplectic Structures on Closed 4-Manifolds
• Symplectic 4-manifolds with fixed point free circle actions