Abstract
Ballico proved that a smooth projective variety X of degree d and dimension m over a finite field of q elements admits a smooth hyperplane section if q≥d(d−1)m. 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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