arXiv math/07037292007-03-28math.AGmath.CV

Curvature semipositivity of relative pluricanonical systems

Hajime Tsuji

备注：: 24pages no figure, Reference up dated and correction on the proof of Theorem 5.5

英文摘要：

We prove semipositivity of the curvature of the Narashimhan-Simha metric on an arbitrary flat projective family of varieties with only canonical singularities. This also implies that the direct image of pluricanonical systems have a natural continuous hermitian strucutre with semipositive curvature curvature current in the sense of Nakano. This is an improvement of the author's preprint ``Refined semipositivity and moduli of canonical models (2005)''.

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