Geodesic
Local cohomology of logarithmic forms
[Cohomologie locale des formes logarithmiques]
Denham, G.1 ; Schenck, H.2 ; Schulze, M.3 ; Wakefield, M.4 ; Walther, U.5
1 University of Western Ontario Department of Mathematics London, Ontario N6A 5B7 (Canada)
2 University of Illinois Department of Mathematics Urbana, IL 61801 (USA)
3 University of Kaiserslautern Department of Mathematics 67663 Kaiserslautern (Germany)
4 United States Naval Academy Department of Mathematics Annapolis, MD 21402 (USA)
5 Purdue University Department of Mathematics West Lafayette, IN 47907 (USA)
Annales de l'Institut Fourier, Tome 63 (2013) no. 3, pp. 1177-1203

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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 : 10.5802/aif.2787
Classification : 32S22, 52C35, 16W25
Keywords: hyperplane arrangement, logarithmic, differential form, free divisor
Mots-clés : arrangements d’hyperplans, forme logarithmique différentielle, diviseur libre

Denham, G. 1 ; Schenck, H. 2 ; Schulze, M. 3 ; Wakefield, M. 4 ; Walther, U. 5

1 University of Western Ontario Department of Mathematics London, Ontario N6A 5B7 (Canada)
2 University of Illinois Department of Mathematics Urbana, IL 61801 (USA)
3 University of Kaiserslautern Department of Mathematics 67663 Kaiserslautern (Germany)
4 United States Naval Academy Department of Mathematics Annapolis, MD 21402 (USA)
5 Purdue University Department of Mathematics West Lafayette, IN 47907 (USA) 
@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},
     pages = {1177--1203},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {63},
     number = {3},
     year = {2013},
     doi = {10.5802/aif.2787},
     zbl = {1277.32030},
     mrnumber = {3137483},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/aif.2787/}
}
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Denham, G.; Schenck, H.; Schulze, M.; Wakefield, M.; Walther, U. Local cohomology of logarithmic forms. Annales de l'Institut Fourier, Tome 63 (2013) no. 3, pp. 1177-1203. doi: 10.5802/aif.2787

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