Leading terms of generalized Plücker formulas
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910500477992960 |
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| author | Juhász, András P. |
| author_facet | Juhász, András P. |
| contents | Generalized Plücker numbers are defined to count certain types of tangent lines of generic degree $d$ complex projective hypersurfaces. They can be computed by identifying them as coefficients of GL(2)-equivariant cohomology classes of certain invariant subspaces, the so-called coincident root strata, of the vector space of homogeneous degree $d$ complex polynomials in two variables. In an earlier paper László M. Fehér and the author gave a new, recursive method for calculating these classes. Using this method, we showed that -- similarly to the classical Plücker formulas counting the bitangents and flex lines of a degree $d$ plane curve -- generalized Plücker numbers are polynomials in the degree $d$.
In this paper, by further analyzing our recursive formula, we determine the leading terms of all the generalized Plücker formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Leading terms of generalized Plücker formulas Juhász, András P. Algebraic Geometry 14N10, 55N91 Generalized Plücker numbers are defined to count certain types of tangent lines of generic degree $d$ complex projective hypersurfaces. They can be computed by identifying them as coefficients of GL(2)-equivariant cohomology classes of certain invariant subspaces, the so-called coincident root strata, of the vector space of homogeneous degree $d$ complex polynomials in two variables. In an earlier paper László M. Fehér and the author gave a new, recursive method for calculating these classes. Using this method, we showed that -- similarly to the classical Plücker formulas counting the bitangents and flex lines of a degree $d$ plane curve -- generalized Plücker numbers are polynomials in the degree $d$. In this paper, by further analyzing our recursive formula, we determine the leading terms of all the generalized Plücker formulas. |
| title | Leading terms of generalized Plücker formulas |
| topic | Algebraic Geometry 14N10, 55N91 |
| url | https://arxiv.org/abs/2404.18859 |