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 $d = d_1+\dots +d_r$.References
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Additional Information
- Carolina Araujo
- Affiliation: IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brazil
- MR Author ID: 702127
- Email: caraujo@impa.br
- Alex Massarenti
- Affiliation: Universidade Federal Fluminense, Rua Mário Santos Braga, 24020-140, Niterói, Rio de Janeiro, Brazil
- Address at time of publication: Dipartimento di Matematica e Informatica, Università di Ferrara, Via Machiavelli 35, 44121 Ferrara, Italy
- MR Author ID: 961373
- Email: alexmassarenti@id.uff.br
- Rick Rischter
- Affiliation: Universidade Federal de Itajubá, Av. BPS 1303, Bairro Pinheirinho, Itajubá, Minas Gerais, Brazil
- MR Author ID: 1240535
- Email: rischter@unifei.edu.br
- Received by editor(s): February 20, 2017
- Received by editor(s) in revised form: June 7, 2017
- Published electronically: August 9, 2018
- Additional Notes: The first named author was partially supported by CNPq and Faperj Research Fellowships.
The second named author is a member of the Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni of the Istituto Nazionale di Alta Matematica “F. Severi” (GNSAGA-INDAM)
The third named author would like to thank CNPq for the financial support. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 2255-2278
- MSC (2010): Primary 14N05, 14N15; Secondary 14E05, 15A69
- DOI: https://doi.org/10.1090/tran/7306
- MathSciNet review: 3896080