The Picard-Lefschetz formula and a conjecture of Kato, the case of Lefschetz fibrations

Details The Picard-Lefschetz formula and a conjecture of Kato, the case of Lefschetz fibrations The Picard-Lefschetz formula and a conjecture of Kato, the case of Lefschetz fibrations

2002-07-05

arxiv.org/abs/math/0207059v1

Mathematics

Algebraic Geometry

Scientific paper

A conjecture of Kato says that the monodromy operator on the cohomology of a
semi-stable degeneration of projective varieties is represented by an algebraic
cycle on the special fiber of a normal crossing model of the fiber product
degeneration. We prove this conjecture in the simple case of a semi-stable
degeneration arising from a Lefschetz fibration.

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