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Secant varieties of toric varieties arising from simplicial complexes

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2020

Autor:innen

Khadam, M. Azeem
Zwiernik, Piotr

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https://doi.org/10.1016/j.laa.2019.12.008
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Linear Algebra and its Applications. Elsevier. 2020, 588, pp. 428-457. ISSN 0024-3795. eISSN 1873-1856. Available under: doi: 10.1016/j.laa.2019.12.008

Zusammenfassung

Motivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affine spaces defined by simplicial complexes. We prove that every such secant is toric, which gives a way to use combinatorial tools to study singularities. We focus on the Segre-Veronese variety for which we completely classify their secants that give Gorenstein or Q-Gorenstein varieties. We conclude providing the explicit description of the singular locus.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Secant variety, Segre-Veronese embedding, Simplicial complex, Cumulants, Singular locus

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ISO 690KHADAM, M. Azeem, Mateusz MICHALEK, Piotr ZWIERNIK, 2020. Secant varieties of toric varieties arising from simplicial complexes. In: Linear Algebra and its Applications. Elsevier. 2020, 588, pp. 428-457. ISSN 0024-3795. eISSN 1873-1856. Available under: doi: 10.1016/j.laa.2019.12.008
BibTex
@article{Khadam2020Secan-52207,
  year={2020},
  doi={10.1016/j.laa.2019.12.008},
  title={Secant varieties of toric varieties arising from simplicial complexes},
  volume={588},
  issn={0024-3795},
  journal={Linear Algebra and its Applications},
  pages={428--457},
  author={Khadam, M. Azeem and Michalek, Mateusz and Zwiernik, Piotr}
}
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