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

Maria Montanucci, Giovanni Zini

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper, we deal with the problem of classifying the genera of quotient curves Hq/G, where Hq is the Fq2 -maximal Hermitian curve and G is an automorphism group of Hq. The groups G considered in the literature fix either a point or a triangle in the plane PG(2, q6). In this paper, we give a complete list of genera of quotients Hq /G, when G ≤ Aut(Hq) ∼= PGU(3,q) does not leave invariant any point or triangle in the plane. Also, the classification of subgroups G of PGU(3,q) satisfying this property is given up to isomorphism.
Original languageEnglish
JournalJournal of Algebraic Combinatorics
Number of pages30
ISSN0925-9899
DOIs
Publication statusPublished - 2019

Keywords

  • Hermitian curve
  • Unitary groups
  • Quotient curves
  • Maximal curves

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