{
  "id": "2404.18859",
  "version": "v1",
  "published": "2024-04-29T16:50:15.000Z",
  "updated": "2024-04-29T16:50:15.000Z",
  "title": "Leading terms of generalized Plücker formulas",
  "authors": [
    "András P. Juhász"
  ],
  "comment": "21 pages, 6 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "Generalized Pl\\\"ucker 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 L\\'aszl\\'o M. Feh\\'er and the author gave a new, recursive method for calculating these classes. Using this method, we showed that -- similarly to the classical Pl\\\"ucker formulas counting the bitangents and flex lines of a degree $d$ plane curve -- generalized Pl\\\"ucker 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 Pl\\\"ucker formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-29T16:50:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N10",
      "55N91"
    ],
    "keywords": [
      "generalized plücker formulas",
      "leading terms",
      "coincident root strata",
      "earlier paper laszlo",
      "complex polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}