On secant defectiveness and identifiability of Segre–Veronese varieties

We give an almost asymptotically sharp bound for the non-secant defectiveness and identifiability of Segre–Veronese varieties. We also provide new examples of defective Segre–Veronese varieties, and implement our methods in Magma. Finally, we give two applications of our techniques: we classify possibly singular 2-secant defective toric surfaces and we study secant defectiveness of Losev–Manin spaces.