Lines highly tangent to a hypersurface

Anand Patel; Eric Riedl; Geoffrey Smith; Dennis Tseng

doi:10.1090/proc/17565

January 14, 2026Proceedings of the American Mathematical Society

Lines highly tangent to a hypersurface

View at Publisher

Ask AI

Bookmark

Share

Key Points

The research aims to explore the behavior of lines that are tangent to smooth hypersurfaces in projective space and derive polynomial bounds on contained planes.
Analyzed the geometry of lines intersecting high-order smooth hypersurfaces.
Developed a polynomial upper bound for the number of planes in a degree d hypersurface.
Provided a non-standard proof approach for a result established by Landsberg.
Derived a polynomial upper bound for planes in a smooth degree d hypersurface in P^5.
Demonstrated the effectiveness of the proposed methods compared to traditional proof techniques.

Ask about this paper

Answers are grounded in this paper and cite their sources.

Implication

Studies lines meeting a smooth hypersurface, providing insights into polynomial bounds on planes contained within.

Abstract

We study spaces of lines that meet a smooth hypersurface X X in P n 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 P^5 and provide a proof of a result of Landsberg without using moving frames.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Patel et al. (2026) studied this question.

synapsesocial.com/papers/6969d4a2940543b9777098f5 https://doi.org/10.1090/proc/17565

View at Publisher

Ask AI

Bookmark

Share

Lines highly tangent to a hypersurface

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Lines highly tangent to a hypersurface

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading