Inherited conics in Hall planes

Aart Blokhuis, István Kovács, Gábor P. Nagy (Corresponding author), Tamás Szőnyi

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The existence of ovals and hyperovals is an old question in the theory of non-Desarguesian planes. The aim of this paper is to describe when a conic of PG(2,q) remains an arc in the Hall plane obtained by derivation. Some combinatorial properties of the inherited conics are obtained also in those cases when it is not an arc. The key ingredient of the proof is an old lemma by Segre–Korchmáros on Desargues configurations with perspective triangles inscribed in a conic.

Original languageEnglish
Pages (from-to)1098-1107
Number of pages10
JournalDiscrete Mathematics
Issue number4
Publication statusPublished - 1 Apr 2019


  • Arcs
  • Finite projective planes
  • Hall planes


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