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A note on rational normal curves totally tangent to a Hermitian variety

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Abstract

Let q be a power of a prime integer p, and let X be a Hermitian variety of degree q + 1 in the n-dimensional projective space. We count the number of rational normal curves that are tangent to X at distinct q + 1 points with intersection multiplicity n. This generalizes a result of Segre on the permutable pairs of a Hermitian curve and a smooth conic.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan

    Ichiro Shimada

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  1. Ichiro Shimada
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Correspondence to Ichiro Shimada.

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Communicated by G. Korchmaros.

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Shimada, I. A note on rational normal curves totally tangent to a Hermitian variety. Des. Codes Cryptogr. 69, 299–303 (2013). https://doi.org/10.1007/s10623-012-9662-x

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  • DOI: https://doi.org/10.1007/s10623-012-9662-x

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