Some consequences of perversity of vanishing cycles
[Quelques conséquences de la perversité des cycles évanescents]
Dimca, Alexandru ; Saito, Morihiko
Annales de l'Institut Fourier, Tome 54 (2004), p. 1769-1792 / Harvested from Numdam
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Pour une fonction holomorphe sur une variété lisse complexe, nous montrons que l'annulation de la cohomologie en bas degré en un point est déterminée par celle aux points voisins, via la perversité du complexe des cycles évanescents. Nous calculons explicitement cet ordre d'annulation lorsque les singularités voisines sont à croisements normaux. Nous en déduisons des résultats sur la taille des blocs de Jordan de la monodromie.

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.

Publié le : 2004-01-01
DOI : https://doi.org/10.5802/aif.2065
Classification:  14B05,  14D05,  14F17,  32S20,  32S25,  32S40,  32S55
Mots clés: fibration de Milnor, faisceau pervers, cycles évanescents 
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     author = {Dimca, Alexandru and Saito, Morihiko},
     title = {Some consequences of perversity of vanishing cycles},
     journal = {Annales de l'Institut Fourier},
     volume = {54},
     year = {2004},
     pages = {1769-1792},
     doi = {10.5802/aif.2065},
     mrnumber = {2134223},
     zbl = {1070.14011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2004__54_6_1769_0}
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Dimca, Alexandru; Saito, Morihiko. Some consequences of perversity of vanishing cycles. Annales de l'Institut Fourier, Tome 54 (2004) pp. 1769-1792. doi : 10.5802/aif.2065. http://gdmltest.u-ga.fr/item/AIF_2004__54_6_1769_0/

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