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

2012/03/19 by Ichiro Shimada, Shimada, Ichiro
Mathematics · Social Sciences · #14M99 #51E20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.1203.4047

openalex publication_date 2012/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 B. Segre on the permutable pairs of a Hermitian curve and a smooth conic.

Citations

• Lattices of Algebraic Cycles on Fermat Varieties in Positive Characteristics

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