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...g(V ) (see [Bom-Zan 1995], [Dav-Phi 1999], [Sch 1996]). Let us define the obstruction index ω(V ) as the minimum degree of an hypersurface containing V . We remark that ω(V ) ≤ n deg(V )1/ codim(V ) (=-=[Cha]-=-). Assume that V is not transverse (i. e. is not contained in a translate of a subtorus). In [Amo-Dav 2003] we conjecture µ̂ess(V ) ≥ c(n)ω(V )−1 for some c(n) > 0 and we prove µ̂ess(V ) ≥ c(n)ω(V )−1...