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

Takahisa Sasajima; Toru Ohmoto

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

Algebraic Geometry 2017-08-17 v3 Algebraic Topology

Authors: Takahisa Sasajima , Toru Ohmoto

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.

Keywords

universal polynomials local singularities multi-singularities enumerative formulae projective surfaces projective 3-folds ordinary singularities weighted euler characteristics

Cite

@article{arxiv.1606.09138,
  title  = {Classical formulae on projective surfaces and $3$-folds with ordinary singularities, revisited},
  author = {Takahisa Sasajima and Toru Ohmoto},
  journal= {arXiv preprint arXiv:1606.09138},
  year   = {2017}
}

Comments

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

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

Abstract

Keywords

Cite

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