Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planes
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Títol
Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planesData de publicació
2012-02Editor
Springer USISSN
0925-1022; 1573-7586Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
http://link.springer.com/article/10.1007/s10623-012-9624-3Versió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
The existence of certain monomial hyperovals D(xk) in the finite Desarguesian projective plane PG(2, q), q even, is related to the existence of points on certain projective plane curves gk(x, y, z). Segre showed that ... [+]
The existence of certain monomial hyperovals D(xk) in the finite Desarguesian projective plane PG(2, q), q even, is related to the existence of points on certain projective plane curves gk(x, y, z). Segre showed that some values of k (k = 6 and 2i) 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 gk. [-]
Publicat a
Designs, Codes and Cryptography. December 2012, Volume 65, Issue 3Drets d'accés
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