On secant defectiveness and identifiability of Segre–Veronese varieties

Abstract

We give Margin NotesMargin notes provide warnings and explanations regarding changes in the text. No need to respond to these notes unless you disagree with the change. However, please respond to queries (if any).Red parts indicate major changes! Please check them carefully.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.