Pencils of binary quartics
Polynomial bounds for the oscillation of solutions of Fuchsian systems
We study the problem of placing effective upper bounds for the number of zeroes of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound, polynomially growing on the frontier of the class of Fuchsian systems of a given dimension having singular points. As a function of , this bound turns out to be double exponential in the precise sense explained in the paper.As a corollary, we obtain a solution of the so-called restricted infinitesimal...
Polynomial-time computation of the degree of a dominant morphism in zero characteristic. II.
Puiseux Expansion of a Cuspidal Singularity
We present an effective and elementary method of determining the topological type of a cuspidal plane curve singularity with given local parametrization.