 
Summary: ON THE DIMENSIONS OF SECANT VARIETIES OF
SEGREVERONESE VARIETIES
HIROTACHI ABO AND MARIA CHIARA BRAMBILLA
Abstract. This paper explores the dimensions of higher secant varieties to
SegreVeronese 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 twofactor SegreVeronese varieties. We
also use these methods to give a complete classification of defective sth Segre
Veronese varieties for small s. In the final section, we propose a conjecture
about defective twofactor SegreVeronese varieties.
1. Introduction
In many applications, it is natural to represent a collection of data as a multi
indexed list. Alternatively, one can think of the data as a multidimensional array.
A mathematical framework that includes the study of multidimensional arrays is
through parameter spaces of tensors.
Every tensor can be written as a linear combination of socalled decomposable
tensors. A tensor is said to have rank s if it can be written as a linear combination
