Discriminant Complements and Kernels of Monodromy Representations
alg-geom
2008-02-03 v3 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.alg-geom/9708002,
title = {Discriminant Complements and Kernels of Monodromy Representations},
author = {James A. Carlson and Domingo Toledo},
journal= {arXiv preprint arXiv:alg-geom/9708002},
year = {2008}
}
Comments
20 page dvi file available at http://www.math.utah.edu/~carlson/eprints.html Minor changes for final version to appear in Duke J. Math