Classical formulae on projective surfaces and $3$-folds with ordinary   singularities, revisited
  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. 
Takahisa Sasajima and Toru Ohmoto
math.AG math.AT