Abstract
Let \(X^n\) be a nonsingular hypersurface of degree \(d\ge 2\) in the projective space \(\mathbb {P}^{n+1}\) defined over a finite field \(\mathbb {F}_q\) of q elements. We prove a Homma–Kim conjecture on a upper bound about the number of \(\mathbb {F}_q\)-points of \(X^n\) for \(n=3\), and for any odd integer \(n\ge 5\) and \(d\le q\).
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Acknowledgements
The author wishes to thank the referees for their suggestions and careful readings of this manuscript. During the preparation of this paper, the author was partially supported by the Project VRID N. 219.015.023-INV.
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Tironi, A.L. On a Homma–Kim conjecture for nonsingular hypersurfaces. Annali di Matematica 201, 617–635 (2022). https://doi.org/10.1007/s10231-021-01131-4
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DOI: https://doi.org/10.1007/s10231-021-01131-4