On generators of the module of logarithmic 1-forms with poles along an arrangement
Journal of Algebraic Combinatorics, Tome 4 (1995) no. 3, pp. 253-269.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: For each element $X$ of codimension two of the intersection lattice of a hyperplane arrangement we define a differential logarithmic 1-forms $ohgr_{ X }$ with poles along the arrangement. Then we describe the class of arrangements for which forms $ohgr_{ X }$ generate the whole module of the logarithmic 1-forms with poles along the arrangement. The description is done in terms of linear relations among the functionals defining the hyperplanes. We construct a minimal free resolution of the module generated by $ohgr_{ X }$ that in particular defines the projective dimension of this module. In order to study relations among $ohgr_{ X }$ we construct free resolutions of certain ideals of a polynomial ring generated by products of linear forms. We give examples and discuss possible generalizations of the results.
Mots-clés : hyperplane arrangement, logarithmic form, module, free resolution, ideal 
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     author = {Yuzvinsky, Sergey},
     title = {On generators of the module of logarithmic 1-forms with poles along an arrangement},
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Yuzvinsky, Sergey. On generators of the module of logarithmic 1-forms with poles along an arrangement. Journal of Algebraic Combinatorics, Tome 4 (1995) no. 3, pp. 253-269. https://geodesic-test.mathdoc.fr/item/JAC_1995__4_3_a0/