Monodromy of Complete Intersections and Surface Potentials

Following Newton, Ivory and Arnold, we study the Newtonian potentials of algebraic hypersurfaces in R. The ramification of (analytic continuations of) these potential depends on a monodromy group, which can be considered as a proper subgroup of the local monodromy group of a complete intersection (acting on a twisted vanishing homology group if n is odd). Studying this monodromy group we prove, in particular, that the attraction force of a hyperbolic layer of degree d in R coincides with appropriate algebraic vector-functions everywhere outside the attracting surface if n = 2 or d = 2, and is non-algebraic in all domains other than the hyperbolicity domain if the surface is generic and (d ≥ 3)&(n ≥ 3)&(n+ d ≥ 8). Recently W. Ebeling removed the last restriction d+n ≥ 8, see his Appendix to this article.