We show that the kernel of the monodromy representation for
hypersurfaces of degree d and dimension n is large for d at
least three with the exception of the cases (d,n) = (3,0) and
(3,1). For these the kernel is finite. By "large" we mean a
group 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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Last modified by jac at 15:52 on 12/27/1997.