On the Cohomology of Fibres of Polynomial Maps
The cohomology groups of the fibres of a polynomial mapping are locally constant except over a finite number of points. The change of the cohomology is caused by singularities if one includes those at infinity. In this paper conditions are given such that the rank of certain cohomology groups is still constant or behaves in a semicontinuous way. For the description of the change of cohomology it is important to look at direct image sheaves. The nature of the change can be understood using notions from the theory of covering projections.
2000 Mathematics Subject ClassificationPrimary 14D05 Secondary 14D06, 55N30
Key words and phrasesPolynomial map atypical fibre direct image sheaf constructible sheaf covering projection
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