A Terracini Lemma for osculating spaces with applications to Veronese   surfaces
  Here we present a partial generalization to higher order osculating spaces of the classical Lemma of Terracini on ordinary tangent spaces. As an application, we investigate the secant varieties to the osculating varieties to the Veronese embeddings of the projective plane. 
Edoardo Ballico and Claudio Fontanari