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Preprint . 2022
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Proceedings of the American Mathematical Society
Article . 2026 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2022
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Lines highly tangent to a hypersurface

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 14 Jan 2026Embargo end date: 01 Aug 2022 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 154, pages 943-956 (issn: 0002-9939, eissn: 1088-6826, Copyright policy )Funded by:NSF | PostDoctoral Research Fel...
Authors: Patel, Anand; Riedl, Eric; Smith, Geoffrey; Tseng, Dennis;

doi: 10.1090/proc/17565 , 10.48550/arxiv.2208.04393

arXiv: 2208.04393

Lines highly tangent to a hypersurface

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.

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Keywords

Mathematics - Algebraic Geometry, FOS: Mathematics, Algebraic Geometry (math.AG)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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