Curvature semipositivity of relative pluricanonical systems

Details Curvature semipositivity of relative pluricanonical systems Curvature semipositivity of relative pluricanonical systems

2007-03-25

arxiv.org/abs/math/0703729v2

Mathematics

Algebraic Geometry

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

Scientific paper

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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