Open Access
Translator Disclaimer
June 2014 The closure of the symplectic cone of elliptic surfaces
M. J. D. Hamilton
J. Symplectic Geom. 12(2): 365-377 (June 2014).


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.


Download Citation

M. J. D. Hamilton. "The closure of the symplectic cone of elliptic surfaces." J. Symplectic Geom. 12 (2) 365 - 377, June 2014.


Published: June 2014
First available in Project Euclid: 29 August 2014

zbMATH: 1306.53071
MathSciNet: MR3210580

Rights: Copyright © 2014 International Press of Boston


Vol.12 • No. 2 • June 2014
Back to Top