The Ramification Divisors for Branched Coverings of IP nk.
We describe the set of points over which a dominant polynomial map is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by .
We investigate an approach of Bass to study the Jacobian Conjecture via the degree of the inverse of a polynomial automorphism over an arbitrary ℚ-algebra.
We study the group of tame automorphisms of a smooth affine -dimensional quadric, which we can view as the underlying variety of . We construct a square complex on which the group admits a natural cocompact action, and we prove that the complex is and hyperbolic. We propose two applications of this construction: We show that any finite subgroup in is linearizable, and that satisfies the Tits alternative.