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.