Hirotachi Abo, Maria Chiara Brambilla
Published 2009-12-22, updated 2011-06-29Version 2
This paper explores the dimensions of higher secant varieties to Segre-Veronese varieties. The main goal of this paper is to introduce two different inductive techniques. These techniques enable one to reduce the computation of the dimension of the secant variety in a high dimensional case to the computation of the dimensions of secant varieties in low dimensional cases. As an application of these inductive approaches, we will prove non-defectivity of secant varieties of certain two-factor Segre-Veronese varieties. We also use these methods to give a complete classification of defective s-th Segre-Veronese varieties for small s. In the final section, we propose a conjecture about defective two-factor Segre-Veronese varieties.
Comments: Revised version. To appear in Annali di Matematica Pura e Applicata
Higher secant varieties of $\mathbb{P}^n \times \mathbb{P}^m$ embedded in bi-degree $(1,d)$
On the prime ideals of higher secant varieties of Veronese embeddings of small degrees
Induction for secant varieties of Segre varieties
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