Classical formulae on projective surfaces and $3$-folds with ordinary singularities, revisited

Abstract

As an application of universal polynomials for local and multi-singularities of maps, we revisit classical enumerative formulae of Salmon-Cayley-Zeuthen for projective surfaces and analogous formulae of Segre-(B.)Severi-Roth for projective $3$-folds. In particular, several examples of actual computation are given using universal polynomials for computing weighted Euler characteristics of singularity loci.

17 pages; (v2) Typo and reference have been corrected; (v3) a minor error in computation has been fixed

References in corpus (1)

• Singularities and Characteristic Classes for Differentiable Maps

Cited by in corpus (1)

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