Monodromy at Infinity and the Weights of Cohomology

Details Monodromy at Infinity and the Weights of Cohomology Monodromy at Infinity and the Weights of Cohomology

2000-02-25

arxiv.org/abs/math/0002214v5

Mathematics

Algebraic Geometry

AMS-TeX, 15 pages; the cohomologically tame case added

Scientific paper

We show that for a polynomial map, the size of the Jordan blocks for the eigenvalue 1 of the monodromy at infinity is bounded by the multiplicity of the reduced divisor at infinity of a good compactification of a general fiber. The existence of such Jordan blocks is related to global invariant cycles of the graded pieces of the weight filtration. These imply some applications to period integrals. We also show that such a Jordan block of size greater than 1 for the graded pieces of the weight filtration is the restriction of a strictly larger Jordan block for the total cohomology group. If there are no singularities at infinity, we have a more precise statement on the monodromy.

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