2024/04/29 by András Juhász, Juhász, András P.
Mathematics · Computer Science · #Mathematical functions and polynomials #Matrix Theory and Algorithms #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2404.18859
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.