## Kodai Mathematical Journal

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

#### Abstract

Let $M \subset \mathbf{R}^{n+2}$ be a two-dimensional complete intersection. We show how to check whether a mapping $f : M \rightarrow \mathbf{R}^2$ 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.

#### Article information

Source
Kodai Math. J., Volume 40, Number 2 (2017), 200-213.

Dates
First available in Project Euclid: 12 July 2017

https://projecteuclid.org/euclid.kmj/1499846594

Digital Object Identifier
doi:10.2996/kmj/1499846594

Mathematical Reviews number (MathSciNet)
MR3680558

Zentralblatt MATH identifier
06775405

#### Citation

Krzyżanowska, Iwona; Nowel, Aleksandra. Criteria for singularities for mappings from two-manifold to the plane. The number and signs of cusps. Kodai Math. J. 40 (2017), no. 2, 200--213. doi:10.2996/kmj/1499846594. https://projecteuclid.org/euclid.kmj/1499846594