Abstract
The algebraic curve associated to an arc in PG(2, q), with q odd, is examined using both properties of the curve itself as well as properties of the arc. The key case of (q − 1)-arcs means that the behaviour of the associated sextic curves needs to be studied. The case of PG(2, 13) is examined in detail. There is a geometric bijection between 12-arcs and their duals. The latter lead to optimal sextic curves; the former lead to sextics whose set of rational points make them ‘look like’ quartics.
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© 2001 Kluwer Academic Publishers
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Giulietti, M., Hirschfeld, J.W.P., Korchmáros, G. (2001). The Desarguesian Plane of Order Thirteen. In: Blokhuis, A., Hirschfeld, J.W.P., Jungnickel, D., Thas, J.A. (eds) Finite Geometries. Developments in Mathematics, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0283-4_10
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DOI: https://doi.org/10.1007/978-1-4613-0283-4_10
Publisher Name: Springer, Boston, MA
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