Displaying similar documents to “Families of differential forms on complex spaces”

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.