  Motivated by Demailly's strategy towards the Kobayashi hyperbolicity
conjecture, we study the action on the k-jets of germs of holomorphic discs in
a complex manifold X of the reparametrization group of k-jets of germs of
biholomorphisms of the source. This reparametrization group is a subgroup of
the general linear group GL(k) which is not reductive, but nonetheless we show
that its invariants for any linear action which extends to GL(k) form a
finitely generated algebra, and give a new geometric description of the
Demailly-Semple algebra of invariant jet differentials.
