NEWTON POLYGONS AND SINGULAR POINTS OF RE AL POLYNOMIAL VECTOR-FIELDS

We classify collections of singular points of generic polynomial vecto r fields of a given degree in the real plane. The answer is that the u pper bounds to the number of singularities and to the total index are the only restrictions. Our solution is based on the Viro method of glu ing of polynomials, which allows to reduce the singularity theory prob lem to a combinatorial question on triangulations of Newton polygons.