Transverse linear subspaces to hypersurfaces over finite fields

Shamil Asgarli; Lian Duan; Kuan-Wen Lai

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arXiv · 2008.11306

Transverse linear subspaces to hypersurfaces over finite fields

Shamil Asgarli·Lian Duan·Kuan-Wen Lai

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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 $q\geq d(d-1)^{\dim X}$. 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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Shamil Asgarli, Lian Duan, Kuan-Wen Lai. 2020-08-25. Transverse linear subspaces to hypersurfaces over finite fields. https://arxiv.org/abs/2008.11306

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