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

Abstract

Dedicated to Professor Piotr Pragacz on the occasion of his 60th birthday.Abstract. We study universal polynomials of characteristic classes associated to the Aclassification of map-germs (C 2 , 0) → (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.

Singularities and Characteristic Classes for Differentiable Maps

“…Given an A-finite singularity type η of maps C m → C n , the singularity locus η(f ) ⊂ X and the bifurcation locus B η (f ) = p 0 (η(f )) ⊂ B are defined. It is not difficult to show the following theorem [63]: Theorem 4.9. Let η be an A-finite singularity type.…”

“…By the restriction method, we can compute tp A for lips, gulls and goose [63]. There are applications of these formulas on projective algebraic geometry of surfaces.…”