Geodesic
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 ohgrX with poles along the arrangement. Then we describe the class of arrangements for which forms ohgrX 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 ohgrX that in particular defines the projective dimension of this module. In order to study relations among ohgrX 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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     year = {1995},
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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/