Monodromy of a family of hypersurfaces containing a given subvariety |
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Authors: | Ania Otwinowska |
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Institution: | Laboratoire de Mathématiques, Université Paris-Sud, Bât. 425, 91405 Orsay cedex, France; RIMS, Kyoto University, Kyoto 606-8502, Japan |
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Abstract: | For a subvariety of a smooth projective variety, consider the family of smooth hypersurfaces of sufficiently large degree containing it, and take the quotient of the middle cohomology of the hypersurfaces by the cohomology of the ambient variety and also by the cycle classes of the irreducible components of the subvariety. Using Deligne's semisimplicity theorem together with Steenbrink's theory for semistable degenerations, we give a simpler proof of the first author's theorem (with a better bound of the degree of hypersurfaces) that this monodromy representation is irreducible. |
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