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

摘要

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.