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

Takahisa Sasajima, Toru Ohmoto

Published 2016-06-29Version 1

As an application of universal polynomials for local and multi-singularities of maps, we revisit classical formulae of Salmon-Cayley-Zeuthen for projective surfaces and analogous formulae of Segre-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.