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This paper explores the dimensions of higher secant varieties toSegre-Veronese varieties. The main goal of this paper is to introduce twodifferent inductive techniques. These techniques enable one to reduce thecomputation of the dimension of the secant variety in a high dimensional caseto the computation of the dimensions of secant varieties in low dimensionalcases. As an application of these inductive approaches, we will provenon-defectivity of secant varieties of certain two-factor Segre-Veronesevarieties. We also use these methods to give a complete classification ofdefective s-th Segre-Veronese varieties for small s. In the final section, wepropose a conjecture about defective two-factor Segre-Veronese varieties.

On the dimensions of secant varieties of Segre-Veronese varieties