Transverse linear subspaces to hypersurfaces over finite fields

2020/08/25 by Shamil Asgarli, Lian Duan, Asgarli, Shamil +3
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2008.11306

Abstract

Ballico proved that a smooth projective variety X of degree d over a finite field of q elements admits a smooth hyperplane section if q≥ d(d-1)^{dim X}. In this paper, we refine this criterion for higher codimensional linear sections on smooth hypersurfaces and for hyperplane sections on Frobenius classical hypersurfaces. We also prove a similar result for the existence of reduced hyperplane sections on reduced hypersurfaces.

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