Work

Quadratic counts of highly tangent lines to hypersurfaces

Year: 2025

Type: article

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 a quadratic form‐valued Euler number that depends on a choice of orientation.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.70048

Authors: Stephen McKean, Giosuè Muratore, Wern Juin Gabriel Ong

Institutions: Brigham Young University, University of Lisbon, Universidade Lusófona, University of Bonn

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Fundação para a Ciência e a Tecnologia

Awards: G4747736532, PostDoctoral Research Fellowship