Classical formulae on projective surfaces and $3$-folds with ordinary singularities, revisited
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Publication:5354675
zbMATH Open1388.14143arXiv1606.09138MaRDI QIDQ5354675
Takahisa Sasajima, Toru Ohmoto
Publication date: 4 September 2017
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 -folds. In particular, several examples of actual computation are given using universal polynomials for computing weighted Euler characteristics of singularity loci.
Full work available at URL: https://arxiv.org/abs/1606.09138
Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Global theory of complex singularities; cohomological properties (32S20) Classical problems, Schubert calculus (14N15)
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