Arc (projective geometry)

Loosely speaking, they are sets of points that are far from "line-like" in a plane or far from "plane-like" in a three-dimensional space.

An important generalization of k-arcs, also referred to as arcs in the literature, is the (k, d)-arcs.

Every conic in the Desarguesian projective plane PG(2,q), i.e., the set of zeros of an irreducible homogeneous quadratic equation, is an oval.

Thus, every oval can be uniquely extended to a hyperoval in a finite projective plane of even order.

In the Desarguesian projective planes, PG(2,q), no q-arc is complete, so they may all be extended to ovals.