Transverse linear subspaces to hypersurfaces over finite fields

DOI10.1016/j.ffa.2024.102396arXiv2008.11306OpenAlexW4392263583MaRDI QIDQ6150627

Shamil Asgarli, Lian Duan, Kuan-Wen Lai

Publication date: 6 March 2024

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.11306

zbMATH Keywords

finite fieldshypersurfacesBertini's theoremFrobenius classicality

Mathematics Subject Classification ID

Finite ground fields in algebraic geometry (14G15) Projective techniques in algebraic geometry (14N05) Hypersurfaces and algebraic geometry (14J70)

Cites Work

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• Polar varieties, Bertini's theorems and number of points of singular complete intersections over a finite field
• Explicit estimates for the number of rational points of singular complete intersections over a finite field
• Bernoulli's inequality
• Space filling curves over finite fields
• An elementary bound for the number of points of a hypersurface over a finite field
• Bertini theorems over finite fields
• Transverse lines to surfaces over finite fields
• A Bertini type theorem for pencils over finite fields
• An upper bound on the number of rational points of arbitrary projective varieties over finite fields
• An effective Bertini theorem over finite fields
• Sharp Bertini Theorem for Plane Curves over Finite Fields

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