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 a quadratic form‐valued Euler number that depends on a choice of orientation.
Authors
- Wern Juin Gabriel Ong (ORCID: https://orcid.org/0000-0002-4955-5205)
- Stephen McKean (ORCID: https://orcid.org/0000-0002-0863-6084)
- Giosuè Muratore (ORCID: https://orcid.org/0000-0003-0038-1432)
Institutions
- Brigham Young University (US)
- University of Bonn (DE)
- University of Lisbon (PT)
- Universidade Lusófona (PT)
Publication Details
- Journal
- Mathematische Nachrichten
- Published
- 2025-10-07
- DOI
- https://doi.org/10.1002/mana.70048
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00