Journal of Symplectic Geometry
- J. Symplectic Geom.
- Volume 12, Number 2 (2014), 365-377.
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 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.
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. https://projecteuclid.org/euclid.jsg/1409317933