Journal of Symplectic Geometry

The closure of the symplectic cone of elliptic surfaces

M. J. D. Hamilton

Full-text: Open access

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 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.

Article information

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

Dates
First available in Project Euclid: 29 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1409317933

Mathematical Reviews number (MathSciNet)
MR3210580

Zentralblatt MATH identifier
1306.53071

Citation

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


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