Semiarcs with a long secant in $\mathrm{PG}(2,q)$

Bence Csajbók, Tamás Héger, György Kiss

A $t$-semiarc is a pointset ${\mathcal{S}}_t$ with the property that the number of tangent lines to ${\mathcal{S}}_t$ at each of its points is $t$. We show that if a small $t$-semiarc ${\cal…