Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planes
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http://dx.doi.org/10.1007/s10623-012-9624-3 |
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Title
Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planesDate
2012-02Publisher
Springer USISSN
0925-1022; 1573-7586Type
info:eu-repo/semantics/articlePublisher version
http://link.springer.com/article/10.1007/s10623-012-9624-3Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
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. [-]
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Designs, Codes and Cryptography. December 2012, Volume 65, Issue 3Rights
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