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arXiv · 2111.09578

Curves on Frobenius classical surfaces in $\mathbb{P}^3$ over finite fields

Elena Berardini·Jade Nardi
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Abstract

In this paper we give an upper bound on the number of rational points on an irreducible curve $C$ of degree $δ$ defined over a finite field $\mathbb{F}_q$ lying on a Frobenius classical surface $S$ embedded in $\mathbb{P}^3$. This leads us to investigate arithmetic properties of curves lying on surfaces. In a certain range of $δ$ and $q$, our result improves all other known bounds in the context of space curves.

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Elena Berardini, Jade Nardi. 2022-05-13. Curves on Frobenius classical surfaces in $\mathbb{P}^3$ over finite fields. https://arxiv.org/abs/2111.09578

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