Almost Kähler forms on rational 4-manifolds

Tianjun Li University of Minnesota Weiyi Zhang University of Warwick

Algebraic Geometry Complex Variables and Complex Analysis Symplectic Geometry mathscidoc:1705.01001

Amer. J. Math., 137, (5), 1209–1256, 2015
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-currentform 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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@inproceedings{tianjun2015almost,
  title={Almost Kähler forms on rational 4-manifolds},
  author={Tianjun Li, and Weiyi Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170530145921482366765},
  booktitle={Amer. J. Math.},
  volume={137},
  number={5},
  pages={1209–1256},
  year={2015},
}
Tianjun Li, and Weiyi Zhang. Almost Kähler forms on rational 4-manifolds. 2015. Vol. 137. In Amer. J. Math.. pp.1209–1256. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170530145921482366765.
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