Almost Kahler forms on rational 4-manifolds

Abstract

We study Nakai-Moishezon type question and Donaldson's "tamed to compatible" question for almost complex structures on rational four manifolds. By extending Taubes' subvarieties--current--form technique to $J-$nef genus $0$ classes, we give affirmative answers of these two questions for all tamed almost complex structures on $S^2$ bundles over $S^2$ as well as for many geometrically interesting tamed almost complex structures on other rational four manifolds, including the del Pezzo ones.

46 pages. v2, introduction shortened, mistakes corrected. arXiv admin note: text overlap with arXiv:0910.5440 by other authors

References in corpus (3)

• The Calabi-Yau equation, symplectic forms and almost complex structures
• Almost Kähler structures on four dimensional unimodular Lie algebras
• J-holomorphic curves in a nef class

Cited by in corpus (4)

• $C^{2,\alpha }$ estimates for nonlinear elliptic equations in complex and almost complex geometry
• J-holomorphic curves in a nef class
• The curve cone of almost complex 4-manifolds
• A note on tame/compatible almost complex structures on four-dimensional Lie algebras