Invariance of Plurigenera

Details Invariance of Plurigenera Invariance of Plurigenera

1997-12-15

arxiv.org/abs/alg-geom/9712016v1

Mathematics

Algebraic Geometry

13 pages, LaTeX file

Scientific paper

10.1007/s002220050276

The following conjecture on the deformation invariance of plurigenera is proved. For a smooth projective holomorphic family of compact complex manifolds over the open unit 1-disk such that all the fibers are of general type, every plurigenus of the fiber is independent of the fiber. The proof uses Nadel's multiplier ideal sheaves, Skoda's result on the generation of ideals with L2 estimates with respect to a plurisubharmonic weight, and the extension theorem of Ohsawa-Takegoshi-Manivel for holomorphic top-degree forms which are L2 with respect to a plurisubharmonic weight.

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