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On the secant varieties to the tangential varieties of a Veronesean

Authors: M. V. Catalisano, A. V. Geramita and A. Gimigliano
Journal: Proc. Amer. Math. Soc. 130 (2002), 975-985
MSC (2000): Primary 14N15; Secondary 14M12
Published electronically: October 12, 2001
MathSciNet review: 1873770
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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.

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Additional Information

M. V. Catalisano
Affiliation: D.I.M.E.T., Università di Genova, P.le Kennedy, 16129 Genova, Italy

A. V. Geramita
Affiliation: Department of Mathematics, Queen’s University, Kingston, Ontario, Canada K7L 3N6 and Dipartimento di Matematica, Università di Genova, 16146 Genova, Italy

A. Gimigliano
Affiliation: Dipartimento di Matematica, Università di Bologna, 40126 Bologna, Italy

Received by editor(s): February 25, 2000
Received by editor(s) in revised form: October 26, 2000
Published electronically: October 12, 2001
Additional Notes: The first author was supported in part by MURST funds.
The second author was supported in part by MURST funds, and by the Natural Sciences and Engineering Research Council of Canada.
The third author was supported in part by the University of Bologna, funds for selected research topics, and by the P.R.R.N.I. “Geometria Algebrica e Algebra Commutativa".
Communicated by: Michael Stillman
Article copyright: © Copyright 2001 American Mathematical Society