Johannes Gmainer

Learn More
Each normal rational curve Γ in PG(n, F ) admits a group PΓL(Γ) of automorphic collineations. It is well known that for characteristic zero only the empty and the entire subspace are PΓL(Γ)–invariant. In case of characteristic p > 0 there may be further invariant subspaces. For #F ≥ n+ 2, we give a construction of all PΓL(Γ)–invariant subspaces. It turns(More)
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(More)
Let be Cayley’s ruled cubic surface in a projective three-space over any commutative field . We determine all collineations fixing , as a set, and all cubic forms defining . For both problems the cases turn out to be exceptional. On the other hand, if then the set of simple points of can be endowed with a non-symmetric distance function. We describe the(More)
  • 1