Displaying similar documents to “Counting solutions of decomposable form equations”

Spaces of polynomials with roots of bounded multiplicity

M. Guest, A. Kozlowski, K. Yamaguchi (1999)

Fundamenta Mathematicae

Similarity:

We describe an alternative approach to some results of Vassiliev ([Va1]) on spaces of polynomials, by applying the "scanning method" used by Segal ([Se2]) in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own right.

A Nielsen theory for intersection numbers

Christopher McCord (1997)

Fundamenta Mathematicae

Similarity:

Nielsen theory, originally developed as a homotopy-theoretic approach to fixed point theory, has been translated and extended to various other problems, such as the study of periodic points, coincidence points and roots. In this paper, the techniques of Nielsen theory are applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f,g), is introduced, and shown to have many of the properties analogous to those of the Nielsen fixed point number....