Work

Lines highly tangent to a hypersurface

Year: 2026

Type: article

Abstract: We study spaces of lines that meet a smooth hypersurface X X in P n \mathbf {P}^n to high order. As an application, we give a polynomial upper bound on the number of planes contained in a smooth degree d d hypersurface in P 5 \mathbf {P}^5 and provide a proof of a result of Landsberg without using moving frames.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17565

Authors: Anand Patel, Eric Riedl, Geoffrey Smith, Dennis Tseng

Institutions: Oklahoma State University, University of Notre Dame, University of Illinois Chicago, Harvard University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: PostDoctoral Research Fellowship, G2276703761