Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Secant varieties of $ {\mathbb{P}^1}\times \cdots \times {\mathbb{P}^1}$ ($ n$-times) are NOT defective for $ n \geq 5$


Authors: Maria Virginia Catalisano, Anthony V. Geramita and Alessandro Gimigliano
Journal: J. Algebraic Geom. 20 (2011), 295-327
DOI: https://doi.org/10.1090/S1056-3911-10-00537-0
Published electronically: March 25, 2010
MathSciNet review: 2762993
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Abstract | References | Additional Information

Abstract: Let $ V_n$ be the Segre embedding of $ {\mathbb{P}^1}\times \cdots \times {\mathbb{P}^1}$ ($ n$ times). We prove that the higher secant varieties $ \sigma_s(V_n)$ always have the expected dimension, except for $ \sigma_3(V_4)$, which is of dimension 1 less than expected.


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Maria Virginia Catalisano
Affiliation: DIPTEM - Dipartimento di Ingegneria della Produzione, Termoenergetica e Modelli Matematici, Piazzale Kennedy, pad. D 16129 Genoa, Italy
Email: catalisano@diptem.unige.it

Anthony V. Geramita
Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada, and Dipartimento di Matematica, Università di Genova,Genoa, Italy
Email: anthony.geramita@gmail.com

Alessandro Gimigliano
Affiliation: Dipartimento di Matematica and CIRAM, Università di Bologna, 40126 Bologna, Italy
Email: gimiglia@dm.unibo.it

DOI: https://doi.org/10.1090/S1056-3911-10-00537-0
Received by editor(s): September 27, 2008
Received by editor(s) in revised form: March 12, 2009
Published electronically: March 25, 2010

American Mathematical Society