Journal of Symplectic Geometry

The closure of the symplectic cone of elliptic surfaces

M. J. D. Hamilton

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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 Kähler 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.

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J. Symplectic Geom., Volume 12, Number 2 (2014), 365-377.

First available in Project Euclid: 29 August 2014

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Hamilton, M. J. D. The closure of the symplectic cone of elliptic surfaces. J. Symplectic Geom. 12 (2014), no. 2, 365--377.

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