On non-secant defectivity of Segre-Veronese varieties

Araujo, Carolina; Massarenti, Alex; Rischter, Rick

doi:10.1090/tran/7306

On non-secant defectivity of Segre-Veronese varieties
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by Carolina Araujo, Alex Massarenti and Rick Rischter PDF

Trans. Amer. Math. Soc. 371 (2019), 2255-2278 Request permission

Abstract:

Let $SV^{\pmb n}_{\pmb d}$ be the Segre-Veronese variety given as the image of $\mathbb {P}^{n_1}\times \dots \times \mathbb {P}^{n_r}$ under the embedding induced by the complete linear system $\big |\mathcal {O}_{\mathbb {P}^{n_1}\times \dots \times \mathbb {P}^{n_r}}(d_1,\dots , d_r)\big |$. We prove that asymptotically $SV^{\pmb n}_{\pmb d}$ is not $h$-defective for $h\leq (\min \{n_i\})^{\lfloor \log _2(d-1)\rfloor }$, where $d = d_1+\dots +d_r$.

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