On a Homma-Kim conjecture for nonsingular hypersurfaces

2020/03/05 by Tironi, Andrea Luigi
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.02951

Abstract

Let Xⁿ be a nonsingular hypersurface of degree d≥ 2 in the projective space ℙⁿ⁺¹ defined over a finite field \mathbbF_q of q elements. We prove a Homma-Kim conjecture on a upper bound about the number of \mathbbF_q-points of Xⁿ for n=3, and for any odd integer n≥ 5 and d≤ q.

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