Displaying similar documents to “Monodromy of a family of hypersurfaces containing a given subvariety”

Some consequences of perversity of vanishing cycles

Alexandru Dimca, Morihiko Saito (2004)

Annales de l’institut Fourier

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For a holomorphic function on a complex manifold, we show that the vanishing cohomology of lower degree at a point is determined by that for the points near it, using the perversity of the vanishing cycle complex. We calculate this order of vanishing explicitly in the case the hypersurface has simple normal crossings outside the point. We also give some applications to the size of Jordan blocks for monodromy.

A geometric application of Nori’s connectivity theorem

Claire Voisin (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study (rational) sweeping out of general hypersurfaces by varieties having small moduli spaces. As a consequence, we show that general K -trivial hypersurfaces are not rationally swept out by abelian varieties of dimension at least two. As a corollary, we show that Clemens’ conjecture on the finiteness of rational curves of given degree in a general quintic threefold, and Lang’s conjecture saying that such varieties should be rationally swept-out by abelian varieties, contradict. ...