Local cohomology of logarithmic forms
Annales de l'Institut Fourier, Volume 63 (2013) no. 3, p. 1177-1203
Let Y be a divisor on a smooth algebraic variety X. We investigate the geometry of the Jacobian scheme of Y, homological invariants derived from logarithmic differential forms along Y, and their relationship with the property that Y be a free divisor. We consider arrangements of hyperplanes as a source of examples and counterexamples. In particular, we make a complete calculation of the local cohomology of logarithmic forms of generic hyperplane arrangements.
Soit X une variété algébrique lisse et Y un diviseur sur X. Nous étudions la géométrie du schéma Jacobien de Y, les invariants homologiques provenant des formes différentielles logarithmiques le long de Y, et leur relation avec la propriété que Y soit un diviseur libre. Nous considérons les arrangements d’hyperplans comme source d’exemples et de contre-exemples. En particulier, nous faisons un calcul complet de la cohomologie locale des formes logarithmiques d’arrangements d’hyperplans génériques.
DOI : https://doi.org/10.5802/aif.2787
Classification:  32S22,  52C35,  16W25
Keywords: hyperplane arrangement, logarithmic, differential form, free divisor
@article{AIF_2013__63_3_1177_0,
     author = {Denham, G. and Schenck, H. and Schulze, M. and Wakefield, M. and Walther, U.},
     title = {Local cohomology of logarithmic forms},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {63},
     number = {3},
     year = {2013},
     pages = {1177-1203},
     doi = {10.5802/aif.2787},
     zbl = {1277.32030},
     mrnumber = {3137483},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2013__63_3_1177_0}
}
Denham, G.; Schenck, H.; Schulze, M.; Wakefield, M.; Walther, U. Local cohomology of logarithmic forms. Annales de l'Institut Fourier, Volume 63 (2013) no. 3, pp. 1177-1203. doi : 10.5802/aif.2787. https://aif.centre-mersenne.org/item/AIF_2013__63_3_1177_0/

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