%0 Journal Article
%T Proof of a Conjecture of Segre and Bartocci on Monomial Hyperovals in Projective Planes
%A Fernando Hernando
%A Gary McGuire
%J Mathematics
%D 2010
%I arXiv
%X The existence of certain monomial hyperovals $D(x^k)$ in the finite Desarguesian projective plane $PG(2,q)$, $q$ even, is related to the existence of points on certain projective plane curves $g_k(x,y,z)$. Segre showed that some values of $k$ ($k=6$ and $2^i$) give rise to hyperovals in $PG(2,q)$ for infinitely many $q$. Segre and Bartocci conjectured that these are the only values of $k$ with this property. We prove this conjecture through the absolute irreducibility of the curves $g_k$.
%U http://arxiv.org/abs/1010.3965v1