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

DOI:
https://doi.org/10.1090/S0002-9939-01-06251-7

Published electronically:
October 12, 2001

MathSciNet review:
1873770

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Abstract | References | Similar Articles | Additional Information

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

Email:
catalisa@dima.unige.it

**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

Email:
tony@mast.queensu.ca, geramita@dima.unige.it

**A. Gimigliano**

Affiliation:
Dipartimento di Matematica, Università di Bologna, 40126 Bologna, Italy

Email:
gimiglia@dm.unibo.it

DOI:
https://doi.org/10.1090/S0002-9939-01-06251-7

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