Innovations in Incidence Geometry

Semiovals from unions of conics

Jeremy M. Dover and Keith E. Mellinger

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A semioval in a projective plane π is a collection of points O with the property that for every point P of O , there exists exactly one line of π meeting O precisely in the point P . There are many known constructions of and theoretical results about semiovals, especially those that contain large collinear subsets.

In a Desarguesian plane π a conic, the set of zeroes of some nondegenerate quadratic form, is an example of a semioval of size q + 1 that also forms an arc (i.e., no three points are collinear). As conics are minimal semiovals, it is natural to use them as building blocks for larger semiovals. Our goal in this work is to classify completely the sets of conics whose union forms a semioval.

Article information

Innov. Incidence Geom., Volume 12, Number 1 (2011), 61-83.

Received: 4 June 2010
First available in Project Euclid: 28 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51E20: Combinatorial structures in finite projective spaces [See also 05Bxx]

semioval conic


Dover, Jeremy M.; Mellinger, Keith E. Semiovals from unions of conics. Innov. Incidence Geom. 12 (2011), no. 1, 61--83. doi:10.2140/iig.2011.12.61.

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