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2 results

  • Monodromy at Infinity and the Weights of Cohomology

  • Alexandru Dimca, Morihiko Saito
  • Journal:
    Compositio Mathematica / Volume 138 / Issue 1 / August 2003
    Published online by Cambridge University Press:
    04 December 2007, pp. 55-71
    Print publication:
    August 2003
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  • 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.

  • On the Monodromy at Infinity of a Polynomial Map, II

  • R. GARCÍA LÓPEZ
  • Journal:
    Compositio Mathematica / Volume 115 / Issue 1 / January 1999
    Published online by Cambridge University Press:
    04 December 2007, pp. 1-20
    Print publication:
    January 1999
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  • To a polynomial map f : Cn + 1 → C one can attach a monodromy transformation on the complex cohomology of its generic fiber that reflects its asymptotic behaviour. In this paper this transformation is determined for a class of generic polynomials in terms of data attached to projective hypersurfaces with isolated singularities.