Symmetric tensor rank with a tangent vector: a generic uniqueness theorem

Authors:
Edoardo Ballico and Alessandra Bernardi

Journal:
Proc. Amer. Math. Soc. **140** (2012), 3377-3384

MSC (2010):
Primary 14N05, 14M17

Published electronically:
February 22, 2012

MathSciNet review:
2929007

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Abstract | References | Similar Articles | Additional Information

Abstract: Let , , be the order Veronese embedding of . Let be the tangent developable of . For each integer let be the join of and copies of . Here we prove that if , and , then for a general there are uniquely determined and a unique tangent vector of such that is in the linear span of ; i.e. a degree linear form (a symmetric tensor of order ) associated to may be written as

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Additional Information

**Edoardo Ballico**

Affiliation:
Department of Mathematics, University of Trento, 38123 Povo (TN), Italy

Email:
ballico@science.unitn.it

**Alessandra Bernardi**

Affiliation:
GALAAD, INRIA Méditerranée, BP 93, 06902 Sophia Antipolis, France

Email:
alessandra.bernardi@inria.fr

DOI:
http://dx.doi.org/10.1090/S0002-9939-2012-11191-8

Keywords:
Veronese variety,
tangential variety,
join,
weak defectivity

Received by editor(s):
January 26, 2011

Received by editor(s) in revised form:
April 11, 2011

Published electronically:
February 22, 2012

Additional Notes:
The authors were partially supported by CIRM of FBK Trento (Italy), Project Galaad of INRIA Sophia Antipolis Méditerranée (France), Institut Mittag-Leffler (Sweden), Marie Curie: Promoting Science (FP7-PEOPLE-2009-IEF), MIUR and GNSAGA of INdAM (Italy).

Communicated by:
Irena Peeva

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.