The minimal number of singularities of stable maps between surfaces (Q837570)

For a stable smooth map \(f\) of degree \(d\) of a closed connected surface into the sphere, let \(c, i\), and \(n\) denote the number of cusps, fold-curve components, and nodes, respectively. The main result of the paper is the determination of the minimal pair \((i,c+n)\) with respect to the lexicographic order. On the one hand, the proof relies on Euler-characteristic analysis, and on the other hand, on constructing maps with desired properties (with gluing techniques).