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The Orevkov invariant of an affine plane curve
Walter D. Neumann, Paul Norbury
We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the…
Universal abelian covers of surface singularities
Walter D. Neumann, Jonathan Wahl
We discuss the evidence for and implications of a conjecture that the universal abelian cover of a Q-Gorenstein surface singularity with finite local homology (i.e., the singularit…
Universal abelian covers of quotient-cusps
Walter D. Neumann, Jonathan Wahl
The quotient-cusp singularities are isolated complex surface singularities that are double-covered by cusp singularities. We show that the universal abelian cover of such a singula…
Rational polynomials of simple type
Walter D. Neumann, Paul Norbury
We classify two-variable polynomials which are rational of simple type. These are precisely the two-variable polynomials with trivial homological monodromy.
Algorithms for polynomials in two variables
Walter D. Neumann, Penelope G. Wightwick
Vladimir Shpilrain and Jie-Tai Yu have asked for an effective algorithm to decide if two elements of C[x,y] are related by an automorphism of C[x,y]. We describe here an efficient…
Unfolding polynomial maps at infinity
Walter D. Neumann, Paul Norbury
We give a topological model for a polynomial map from $\C^n$ to $\C$ in the neighborhood of a fiber with isolated singularities. This is motivated out of the ``unfolding of links''…