Plücker formulas using equivariant cohomology of coincident root strata
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908286259822592 |
|---|---|
| author | Fehér, László M. Juhász, András P. |
| author_facet | Fehér, László M. Juhász, András P. |
| contents | We give a new method to calculate the universal cohomology classes of coincident root loci. We show a polynomial behavior of them and apply this result to prove that generalized Plücker formulas are polynomials in the degree, just as the classical Plücker formulas counting the bitangents and flexes of a degree $d$ generic plane curve. We establish an upper bound for the degrees of these polynomials, and we calculate the leading terms of those whose degrees reach this upper bound.
We believe that the paper is understandable without detailed knowledge of equivariant cohomology. It may serve as a demonstration of the use of equivariant cohomology in enumerative geometry through the examples of coincident root strata. We also explain how the equivariant method can be "translated" into the traditional non-equivariant method of resolutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06430 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Plücker formulas using equivariant cohomology of coincident root strata Fehér, László M. Juhász, András P. Algebraic Geometry Algebraic Topology 14N10, 55N91 We give a new method to calculate the universal cohomology classes of coincident root loci. We show a polynomial behavior of them and apply this result to prove that generalized Plücker formulas are polynomials in the degree, just as the classical Plücker formulas counting the bitangents and flexes of a degree $d$ generic plane curve. We establish an upper bound for the degrees of these polynomials, and we calculate the leading terms of those whose degrees reach this upper bound. We believe that the paper is understandable without detailed knowledge of equivariant cohomology. It may serve as a demonstration of the use of equivariant cohomology in enumerative geometry through the examples of coincident root strata. We also explain how the equivariant method can be "translated" into the traditional non-equivariant method of resolutions. |
| title | Plücker formulas using equivariant cohomology of coincident root strata |
| topic | Algebraic Geometry Algebraic Topology 14N10, 55N91 |
| url | https://arxiv.org/abs/2312.06430 |