On the spectrum of genera of quotients of the Hermitian curve

2017/03/30 by Maria Montanucci, Montanucci, Maria, Giovanni Zini +1 · 1 citation
Arts and Humanities · Mathematics · #11G20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Historical Studies and Socio-cultural Analysis

paper · pdf · doi:10.48550/arxiv.1703.10592

openalex publication_date 2017/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the genera of quotient curves \mathcal H_q/G of the \mathbb F_q²-maximal Hermitian curve \mathcal H_q, where G is contained in the maximal subgroup \mathcal M_q≤\rm Aut(\mathcal H_q) fixing a pole-polar pair (P,ℓ) with respect to the unitary polarity associated with \mathcal H_q. To this aim, a geometric and group-theoretical description of \mathcal M_q is given. The genera of some other quotients \mathcal H_q/G with G\not≤\mathcal M_q are also computed. Thus we obtain new values in the spectrum of genera of \mathbb F_q²-maximal curves. A plane model for \mathcal H_q/G is obtained when G is cyclic of order p⋅ d, with d a divisor of q+1.

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