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

Caterina Consani·Minhyong Kim
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Abstract

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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Caterina Consani, Minhyong Kim. 2002-07-05. The Picard-Lefschetz formula and a conjecture of Kato, the case of Lefschetz fibrations. https://arxiv.org/abs/math/0207059

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