## Kodai Mathematical Journal

### Apparent contours of stable maps between closed surfaces

Takahiro Yamamoto

#### Abstract

Let $M$ and $N$ be connected and orientable, closed surfaces. For a stable map $\varphi : M \rightarrow N$, denote by $c(\varphi)$ and $n(\varphi)$ the numbers of cusps and nodes of $\varphi$ respectively. In this paper, we determine the minimal number $c(\varphi) + n(\varphi)$ among the apparent contours of degree $d$ stable maps $M \rightarrow N$ whose singular points set consists of one component.

#### Article information

Source
Kodai Math. J., Volume 40, Number 2 (2017), 358-378.

Dates
First available in Project Euclid: 12 July 2017

https://projecteuclid.org/euclid.kmj/1499846602

Digital Object Identifier
doi:10.2996/kmj/1499846602

Mathematical Reviews number (MathSciNet)
MR3680566

Zentralblatt MATH identifier
1384.57018

#### Citation

Yamamoto, Takahiro. Apparent contours of stable maps between closed surfaces. Kodai Math. J. 40 (2017), no. 2, 358--378. doi:10.2996/kmj/1499846602. https://projecteuclid.org/euclid.kmj/1499846602