Thom polynomials in $\mathcal{A}$-classification I: counting singular projections of a surface

Abstract

We study universal polynomials of characteristic classes associated to the $\mathcal{A}$-classification of map-germs $({\mathbb{C}}^2,0)\to ({\mathbb{C}}^n,0)$ $(n=2,3)$, that enable us to systematically generalize enumerative formulae in classical algebraic geometry of projective surfaces in 3 and 4-spaces.