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. also provide new examples defective varieties, implement our methods in Magma. Finally, we two applications techniques: classify possibly singular 2-secant toric surfaces study secant Losev–Manin spaces.