A survey on semiovals

Abstract

A semioval in a finite projective plane is a non-empty pointset S with the property that for every point in $S$ there exists a unique line t_P such that $S \cap t_P = {P}$. This line is called the tangent to S at P. Semiovals arise in several parts of finite geometries: as absolute points of a polarity (ovals, unitals), as special minimal blocking sets (vertexless triangle), in connection with cryptography (determining sets). We survey the results on semiovals and give some new proofs