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arXiv · 1611.02371

Number of points of a nonsingular hypersurface in an odd-dimensional projective space

Masaaki Homma·Seon Jeong Kim
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Abstract

The numbers of $\mathbb{F}_q$-points of nonsingular hypersurfaces of a fixed degree in an odd-dimensional projective space are investigated, and an upper bound for them is given. Also we give the complete list of nonsingular hypersurfaces each of which realizes the upper bound. This is a natural generalization of our previous study of surfaces in projective $3$-space.

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Masaaki Homma, Seon Jeong Kim. 2016-11-08. Number of points of a nonsingular hypersurface in an odd-dimensional projective space. https://arxiv.org/abs/1611.02371

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