Hamiltonian 2-forms in Kähler geometry, II Global classification

@inproceedings{CALDERBANK2004Hamiltonian2I,
  title={Hamiltonian 2-forms in K{\"a}hler geometry, II Global classification},
  author={DAVID M. J. CALDERBANK and PAUL GAUDUCHON and CHRISTINA W. T\ONNESEN-FRIEDMAN},
  year={2004}
}
  • DAVID M. J. CALDERBANK, PAUL GAUDUCHON, CHRISTINA W. TØNNESEN-FRIEDMAN
  • Published 2004
We present a classification of compact Kähler manifolds admitting a hamiltonian 2-form (which were classified locally in part I of this work). This involves two components of independent interest. The first is the notion of a rigid hamiltonian torus action. This natural condition, for torus actions on a Kähler manifold, was introduced locally in part I, but such actions turn out to be remarkably well behaved globally, leading to a fairly explicit classification: up to a blow-up, compact Kähler… CONTINUE READING

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