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.
On the secant varieties to the tangential varieties of a Veronesean / Catalisano M.V.; Geramita A.V.; Gimigliano A.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 130:4(2002), pp. 975-985. [10.1090/S0002-9939-01-06251-7]
On the secant varieties to the tangential varieties of a Veronesean
Gimigliano A.
2002
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
