G. Aleksandr, A. K. Aleksandrov, and . Tsikh, Th??orie des r??sidus de Leray et formes de Barlet sur une intersection compl??te singuli??re, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.333, issue.11, pp.973-978, 2001.
DOI : 10.1016/S0764-4442(01)02166-8

D. Bar78 and . Barlet, Le faisceau ? · X sur un espace analytique X de dimension pure, Fonctions de plusieurs variables complexes, III (Sém. François Norguet, Lecture Notes in Math, vol.67080, issue.3, pp.187-204, 1975.

P. Deligne, Les immeubles des groupes de tresses g???n???ralis???s, Inventiones Mathematicae, vol.4, issue.1, pp.273-302, 1972.
DOI : 10.1007/BF01406236

T. De, J. , and G. Pfister, Local analytic geometry, Advanced Lectures in Mathematics , Friedr, Basic theory and applications. MR 1760953, pp.32001-32004, 2000.

T. De-jong and D. Van-straten, Deformations of the normalization of hypersurfaces, Mathematische Annalen, vol.20, issue.1, pp.527-547, 1990.
DOI : 10.1007/BF01444547

H. Paul, V. Edelman, and . Reiner, Not all free arrangements are K(?, 1), Bull. Amer, Math. Soc. (N.S.), vol.3295, issue.1, pp.61-65, 1995.

E. Faber, Normal crossings in local analytic geometry, 2004.

W. Fulton, On the Fundamental Group of the Complement of a Node Curve, The Annals of Mathematics, vol.111, issue.2, pp.111-407, 1980.
DOI : 10.2307/1971204

M. Granger, D. Mond, and M. Schulze, Free divisors in prehomogeneous vector spaces, Proceedings of the London Mathematical Society, vol.102, issue.5, pp.923-950, 2011.
DOI : 10.1112/plms/pdq046

R. Hartshorne, . Residues, and . Duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard With an appendix by P. Deligne, Lecture Notes in Mathematics, vol.64, issue.20, 1963.

E. J. Looijenga, Isolated singular points on complete intersections, pp.74730332021-1, 1984.
DOI : 10.1017/CBO9780511662720

L. D?ungd?ung, T. , and K. Saito, The local ? 1 of the complement of a hypersurface with normal crossings in codimension 1 is abelian, Ark. Mat, vol.2286, issue.1, pp.1-24, 1984.

R. Piene, Ideals associated to a desingularization, Proc. Summer Meeting, pp.503-517, 1978.
DOI : 10.1017/S0305004100054724

G. Scheja, Fortsetzungss???tze der komplex-analytischen Cohomologie und ihre algebraische Charakterisierung, Mathematische Annalen, vol.139, issue.1, pp.75-94, 1964.
DOI : 10.1007/BF01362668

H. Terao, Arrangements of hyperplanes and their freeness, I, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.27, issue.2, pp.293-312, 1980.

A. K. Tsikh, Weakly holomorphic functions on complete intersections, their holomorphic continuation, Mat. Sb. (N.S.), vol.13389, issue.175 4, pp.429-445, 1987.

]. D. Van-straten, A note on the discriminant of a space curve, manuscripta mathematica, vol.242, issue.1, pp.167-177, 1995.
DOI : 10.1007/BF02570469

M. Granger, L. , and C. Umr, Bd Lavoisier, 49045 Angers, France E-mail address: granger@univ-angers