Monodromy of a family of hypersurfaces containing a given subvariety

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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.
23 pages, minor changes

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Algebraic Geometry, 14D05

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http://salesiana.dossiersoluciones.com/handle/123456789/70975

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0404469
 http://arxiv.org/abs/math/0404469

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arXiv