New examples of defective secant varieties of Segre-Veronese varieties
  We prove the existence of defective secant varieties of three-factor and four-factor Segre-Veronese varieties embedded in certain multi-degree. These defective secant varieties were previously unknown and are of importance in the classification of defective secant varieties of Segre-Veronese varieties with three or more factors. 
Hirotachi Abo, Maria Chiara Brambilla
math.AG