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
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

Anthony V. Geramita
Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada, and Dipartimento di Matematica, Università di Genova,Genoa, Italy
MR Author ID: 72575

Alessandro Gimigliano
Affiliation: Dipartimento di Matematica and CIRAM, Università di Bologna, 40126 Bologna, Italy

Received by editor(s): September 27, 2008
Received by editor(s) in revised form: March 12, 2009
Published electronically: March 25, 2010