Semiarcs with a long secant in PG(2,q)
Bence Csajbók, Tamás Héger, György Kiss · Innovations in incidence geometry · 2015
A t-semiarc is a point set S t with the property that the number of tangent lines to S t at each of its points is t.We show that if a small t-semiarc S t in PG(2, q) has a large collinear subset K, then the tangents to S t at the points of K can be blocked by t points not in K.In fact, we give a more general result for small point sets with less uniform tangent distribution.We show that in PG(2, q) small t-semiarcs are related to certain small blocking sets and give some characterization theorems for small semiarcs with large collinear subsets.