Quadratic counts of highly tangent lines to hypersurfaces

Abstract

We give two geometric interpretations for the local type of a line that is highly tangent to a hypersurface in a single point. One interpretation is phrased in terms of the Wronski map, while the other interpretation relates to the fundamental forms of the hypersurface. These local types are the local contributions of an quadratic form-valued Euler number that depends on a choice of orientation.

arXiv comment19 pages. Final version

References in corpus (8)

• An Arithmetic Count of the Lines on a Smooth Cubic Surface
• An arithmetic enrichment of Bézout's Theorem
• The trace of the local ${\mathbf{A}}^1$-degree
• An arithmetic count of the lines meeting four lines in P^3
• Relative Gromov-Witten and maximal contact conics
• An arithmetic count of osculating lines
• On fundamental forms and osculating bundles
• Arithmetic inflection of superelliptic curves