ar X iv : a lg - g eo m / 9 70 80 02 v 1 1 A ug 1 99 7 Discriminant Complements and Kernels of Monodromy Representations
نویسنده
چکیده
Let Φ d,n be the fundamental group of the space of smooth projective hypersurfaces of degree d and dimension n and let ρ be its natural monodromy representation. Then the kernel of ρ is large for d ≥ 3 with the exception of the cases (d, n) = (3, 0), (3, 1). For these and for d < 3 the kernel is finite. A large group is one that admits a homomorphism to a semisimple Lie group of noncompact type with Zariski-dense image. By the Tits alternative a large group contains a free subgroup of rank two.
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