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 (i.e. up to right-left equivalence) of holomorphic map-germs $({\mathbb{C}}^2,0)\to ({\mathbb{C}}^n,0)$ $(n=2,3)$. That enables us to systematically treat with classical enumerative problems of lines of prescribed contact with a given projective surface in $3$ and $4$-spaces.

22 pages; (v2) Typos have been fixed. Section 3.1 has been rewritten more precisely

References in corpus (5)

• Characteristic Classes of Hypersurfaces and Characteristic Cycles
• Specialization of motivic Hodge-Chern classes
• Projective classification of jets of surfaces in 3-space
• Projective classification of jets of surfaces in ${\mathbb{P}}^4$
• Classical formulae on projective surfaces and $3$-folds with ordinary singularities, revisited