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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1209-1256
Launched on MUSE
2015-09-28
Open Access
No
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