Remarks on Projective Algebraic Fiber Spaces Over Curves: Communications in Algebra: Vol 34, No 9

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Abstract

Let f:X → C be a fibration over curve C with general fiber F. Some numerical characteristics of h ⁱ(_X) in terms of h ⁱ (_F), the genus g(C) and the degree of direct image sheaves R ⁱ f _∗ (ω_X/C) are given. If f is the derived fibration induced by m-canonical map, further numerical characterizations of m-plurigenus of F are given.

ACKNOWLEDGMENT

I would like to thank Prof. Meng Chen for useful discussions and generous helps.

Notes

Communicated by L. Ein.

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Remarks on Projective Algebraic Fiber Spaces Over Curves

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