Local cohomology of logarithmic forms

Denham, G.; Schenck, H.; Schulze, M.; Wakefield, M.; Walther, U.

doi:10.5802/aif.2787

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.

Résumé
Abstract

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.

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.

Reçu le : 2011-03-28
Accepté le : 2011-10-24

MR Zbl

DOI : 10.5802/aif.2787

Classification : 32S22, 52C35, 16W25
Keywords: hyperplane arrangement, logarithmic, differential form, free divisor
Mot clés : arrangements d’hyperplans, forme logarithmique différentielle, diviseur libre

Affiliations des auteurs :

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

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     title = {Local cohomology of logarithmic forms},
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     pages = {1177--1203},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2787/

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