Arc (projective geometry)

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Let π be a finite projective plane (not necessarily Desarguesian) of order q. A (k,d) -arc A (k\leq 1,d\leq 1)is a set of k points of π such that each line intersects A in at most d points, and there is at least one line that does intersect A in d points.

[edit] Special cases

The number of points kin A is at most qd + d − q. When equality occurs, one speak of a maximal arc.

((q + 1,2) -arcs are precisely the ovals and (q + 2,2) -arcs are precisely the hyperovals (which can only occur for even q).

[edit] External links

  • C.M. O'Keefe, "Arc" SpringerLink Encyclopaedia of Mathematics (2001)
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