Some consequences of perversity of vanishing cycles

Alexandru Dimca[1]; Morihiko Saito

  • [1] Université de Nice-Sophia-Antipolis, Laboratoire J.A. Dieudonné, UMR 6621, Parc Valrose, 06108 Nice Cedex 02 (France), Kyoto University, RIMS, Kyoto 606-8502 (Japan)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 6, page 1769-1792
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Dimca, Alexandru, and Saito, Morihiko. "Some consequences of perversity of vanishing cycles." Annales de l’institut Fourier 54.6 (2004): 1769-1792. <http://eudml.org/doc/116158>.

@article{Dimca2004,
abstract = {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.},
affiliation = {Université de Nice-Sophia-Antipolis, Laboratoire J.A. Dieudonné, UMR 6621, Parc Valrose, 06108 Nice Cedex 02 (France), Kyoto University, RIMS, Kyoto 606-8502 (Japan)},
author = {Dimca, Alexandru, Saito, Morihiko},
journal = {Annales de l’institut Fourier},
keywords = {Milnor fibration; perverse sheaf; vanishing cycles; monodromy; mixed Hodge structures; nearby cycles; vanishing cohomology sheaf},
language = {eng},
number = {6},
pages = {1769-1792},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some consequences of perversity of vanishing cycles},
url = {http://eudml.org/doc/116158},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Dimca, Alexandru
AU - Saito, Morihiko
TI - Some consequences of perversity of vanishing cycles
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 6
SP - 1769
EP - 1792
AB - 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.
LA - eng
KW - Milnor fibration; perverse sheaf; vanishing cycles; monodromy; mixed Hodge structures; nearby cycles; vanishing cohomology sheaf
UR - http://eudml.org/doc/116158
ER -

References

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