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Bibliografske podrobnosti
Main Authors: Hernando, Fernando, McGuire, Gary
Format: Preprint
Izdano: 2010
Teme:
Online dostop:https://arxiv.org/abs/1010.3965
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Kazalo:
  • 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 $g_k$.