Mathematics > Algebraic Geometry
[Submitted on 22 Dec 2009 (v1), last revised 29 Jun 2011 (this version, v2)]
Title:On the dimensions of secant varieties of Segre-Veronese varieties
View PDFAbstract: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.
Submission history
From: Maria Chiara Brambilla [view email][v1] Tue, 22 Dec 2009 09:02:56 UTC (31 KB)
[v2] Wed, 29 Jun 2011 14:32:01 UTC (32 KB)
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