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We prove the existence of Gysin morphisms for hyperplane sections that maynot satisfy the usual hypotheses of the Lefschetz hyperplane theorem. As anapplication, we show the triviality of the Alexander polynomial of a particularclass of non-symmetric line arrangements, thus providing positive evidence fora conjecture of Papadima and Suciu.

Gysin morphisms for non-transversal hyperplane sections with an application to line arrangements