In this article, we characterize the genera of those quotient curves Hq/G of the Fqjavax.xml.bind.JAXBElement@45f83521-maximal Hermitian curve Hq for which either G is contained in the maximal subgroup M1 of Aut(Hq) fixing a self-polar triangle, or q is even and G is contained in the maximal subgroup M2 of Aut(Hq) fixing a pole-polar pair (P, l) with respect to the unitary polarity associated to Hq(Fqjavax.xml.bind.JAXBElement@590af847) In this way, several new values for the genus of a maximal curve over a finite field are obtained. Our results leave just two open cases to provide the complete list of genera of Galois subcovers of the Hermitian curve; namely, the open cases in [4] when G fixes a point P ϵ Hq(Fqjavax.xml.bind.JAXBElement@5b677e2a) and q is even, and the open cases in [33] when G≤M2 and q is odd.
On the classification problem for the genera of quotients of the Hermitian curve / Dalla Volta, F.; Montanucci, M.; Zini, G.. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - 47:12(2019), pp. 4889-4909. [10.1080/00927872.2019.1601733]
On the classification problem for the genera of quotients of the Hermitian curve
Zini G.
2019
Abstract
In this article, we characterize the genera of those quotient curves Hq/G of the Fqjavax.xml.bind.JAXBElement@45f83521-maximal Hermitian curve Hq for which either G is contained in the maximal subgroup M1 of Aut(Hq) fixing a self-polar triangle, or q is even and G is contained in the maximal subgroup M2 of Aut(Hq) fixing a pole-polar pair (P, l) with respect to the unitary polarity associated to Hq(Fqjavax.xml.bind.JAXBElement@590af847) In this way, several new values for the genus of a maximal curve over a finite field are obtained. Our results leave just two open cases to provide the complete list of genera of Galois subcovers of the Hermitian curve; namely, the open cases in [4] when G fixes a point P ϵ Hq(Fqjavax.xml.bind.JAXBElement@5b677e2a) and q is even, and the open cases in [33] when G≤M2 and q is odd.
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