On non-secant defectivity of Segre-Veronese varieties

Abstract

Let $S{V}_d^n$ be the Segre-Veronese given as the image of the embedding induced by the line bundle ${\mathcal{O}}_{{\mathbb{P}}^{n_1}\times \cdots \times {\mathbb{P}}^{n_r}}(d_1,\dots ,d_r)$. We prove that asymptotically $S{V}_d^n$ is not $h$-defective for $h\le n_1^{\lfloor {\log }_2(d-1)\rfloor }$.

23 pages