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Monodromy at infinity and the weights of cohomology. (English) Zbl 1039.32037
The authors prove 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 fibre. In the last part of the paper the authors show interesting applications to the study of period integrals.

##### MSC:
 32S40 Monodromy; relations with differential equations and $$D$$-modules (complex-analytic aspects) 32S20 Global theory of complex singularities; cohomological properties 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
##### Keywords:
monodromy at infinity; hodge structure; vanishing cycle
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