| Institution: | D.I.M.E.T., Università di Genova, P.le Kennedy, 16129 Genova, Italy ; Department of Mathematics, Queen's University, Kingston, Ontario, Canada K7L 3N6 and Dipartimento di Matematica, Università di Genova, 16146 Genova, Italy ; Dipartimento di Matematica, Università di Bologna, 40126 Bologna, Italy |
| Abstract: | We study the dimensions of the higher secant varieties to the tangent varieties of Veronese varieties. Our approach, generalizing that of Terracini, concerns 0-dimensional schemes which are the union of second infinitesimal neighbourhoods of generic points, each intersected with a generic double line. We find the deficient secant line varieties for all the Veroneseans and all the deficient higher secant varieties for the quadratic Veroneseans. We conjecture that these are the only deficient secant varieties in this family and prove this up to secant projective 4-spaces. |
