Almost Kahler forms on rational 4-manifolds

Tian-Jun Li; Weiyi Zhang

Almost Kahler forms on rational 4-manifolds

Symplectic Geometry 2015-07-10 v2 Algebraic Geometry Complex Variables Geometric Topology

Authors: Tian-Jun Li , Weiyi Zhang

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.

Keywords

almost contact manifolds kähler manifolds smooth 4-manifolds

Cite

@article{arxiv.1210.2377,
  title  = {Almost Kahler forms on rational 4-manifolds},
  author = {Tian-Jun Li and Weiyi Zhang},
  journal= {arXiv preprint arXiv:1210.2377},
  year   = {2015}
}

Comments

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

Almost Kahler forms on rational 4-manifolds

Abstract

Keywords

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