Leading terms of generalized Plücker formulas

Abstract

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.

21 pages, 6 figures; typos corrected