On curves lying on a rational normal surface scroll

On the Normal Bundles of Smooth Rational Space Curves

in this note we consider smooth rational curves C of degree n in threedimensional projective space IP 3 (over a closed field of characteristic 0). To avoid trivial exceptions we shall always assume that n ~ 4 (this does not hold however for certain auxiliary curves we shall consider). Let N = N c be the normal bundle of C in IP 3. Since degel(IP3)=4, and d e g c l ( l P 0 = 2 , we have that d e...

Nuclei of Normal Rational Curves

A k–nucleus of a normal rational curve in PG(n, F ) is the intersection over all k–dimensional osculating subspaces of the curve (k ∈ {−1, 0, . . . , n− 1}). It is well known that for characteristic zero all nuclei are empty. In case of characteristic p > 0 and #F ≥ n the number of non–zero digits in the representation of n+ 1 in base p equals the number of distinct nuclei. An explicit formula ...

Completeness of Normal Rational Curves

The completeness of normal rational curves, considered as (q + 1)-arcs in PG(n, q), is investigated. Previous results of Storme and Thas are improved by using a result by Kovacs. This solves the problem completely for large prime numbers q and odd nonsquare prime powers q = p2h+l with p prime, p > po(h), h>\,1where po(h) is an odd prime number which depends on h.

Rational Curves on Varieties

Rational points on curves