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Secant varieties of Segre-Veronese embeddings of \((\mathbb{P }^1)^r\)

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Abstract

We use a double degeneration technique to calculate the dimension of the secant variety of any Segre-Veronese embedding of \((\mathbb P ^1)^r\).

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Acknowledgments

It is a pleasure to thank Giorgio Ottaviani for suggesting us the idea of how to calculate the equation of the secant variety of the \((2,2,2)\)-embedding of \((\mathbb P ^1)^3\). We are pleased as well to thank Chiara Brambilla for many useful conversations.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Antonio Laface

  2. Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern, 0316 , Oslo, Norway

    Elisa Postinghel

Authors
  1. Antonio Laface
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  2. Elisa Postinghel
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Corresponding author

Correspondence to Elisa Postinghel.

Additional information

The first author was supported by Proyecto FONDECYT Regular 2011, N. 1110096. The second author was supported by Marie-Curie IT Network SAGA, [FP7/2007–2013] grant agreement PITN-GA- 2008-214584. Both authors were partially supported by Institut Mittag-Leffler.

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Laface, A., Postinghel, E. Secant varieties of Segre-Veronese embeddings of \((\mathbb{P }^1)^r\) . Math. Ann. 356, 1455–1470 (2013). https://doi.org/10.1007/s00208-012-0890-1

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  • DOI: https://doi.org/10.1007/s00208-012-0890-1

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