On a set of polarized Kähler metrics on algebraic manifolds

@article{Tian1990OnAS,
  title={On a set of polarized K{\"a}hler metrics on algebraic manifolds},
  author={Gang Tian},
  journal={Journal of Differential Geometry},
  year={1990},
  volume={32},
  pages={99-130}
}
  • G. Tian
  • Published 1 July 1990
  • Mathematics
  • Journal of Differential Geometry
A projective algebraic manifold M is a complex manifold in certain projective space CP, N > dim c M = n . The hyperplane line bundle of CP restricts to an ample line bundle L on M. This bundle L is a polarization on M. For the Kahler metric g on M, we can associate a positive, rf-closed (1, l)-form ωg . In any local coordinate system (Zj, , zn) of M , the metric g is expressed by a tensor (^/j)1</ 7-<fI, and ωg is defined to be ^^Σ" j=ι gqdzi Λ d~z.. We call this ω the Kahler form associated to… 
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