Criteria for singularities for mappings from two-manifold to the plane. The number and signs of cusps

Abstract

Let M ⊂ Rⁿ⁺² be a two-dimensional complete intersection. We show how to check whether a mapping f: M → R² is 1-generic with only folds and cusps as singularities. In this case we give an effective method to count the number of positive and negative cusps of a polynomial f, using the signatures of some quadratic forms.