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arXiv · 1502.07941

Maximal curves from subcovers of the GK-curve

Massimo Giulietti·Luciane Quoos·Giovanni Zini
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Abstract

For every $q=n^3$ with $n$ a prime power greater than $2$, the GK-curve is an $\mathbb F_{q^2}$-maximal curve that is not $\mathbb F_{q^2}$-covered by the Hermitian curve. In this paper some Galois subcovers of the GK curve are investigated. We describe explicit equations for some families of quotients of the GK-curve. New values in the spectrum of genera of $\mathbb F_{q^2}$-maximal curves are obtained. Finally, infinitely many further examples of maximal curves that cannot be Galois covered by the Hermitian curve are provided.

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Massimo Giulietti, Luciane Quoos, Giovanni Zini. 2015-02-27. Maximal curves from subcovers of the GK-curve. https://arxiv.org/abs/1502.07941

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