Quotients of the Hermitian curve from subgroups of \rm PGU(3,q) without fixed points or triangles

2018/04/10 by Montanucci, Maria, Zini, Giovanni · 1 citation
#11G20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1804.03398

Abstract

In this paper we deal with the problem of classifying the genera of quotient curves H_q/G, where H_q is the \mathbbF_q²-maximal Hermitian curve and G is an automorphism group of H_q. The groups G considered in the literature fix either a point or a triangle in the plane \rm PG(2,q⁶). In this paper, we give a complete list of genera of quotients H_q/G, when G ≤ \rm Aut(H_q) ≅ \rm PGU(3,q) does not leave invariant any point or triangle in the plane. As a result, the classification of subgroups G of \rm PGU(3,q) satisfying this property is given up to isomorphism.

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