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Secant Cumulants and Toric Geometry

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2015

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Oeding, Luke
Zwiernik, Piotr

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https://doi.org/10.1093/imrn/rnu056
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http://arxiv.org/abs/1212.1515v2

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International Mathematics Research Notices (IMRN). Oxford University Press (OUP). 2015, 2015(12), pp. 4019-4063. ISSN 1073-7928. eISSN 1687-0247. Available under: doi: 10.1093/imrn/rnu056

Zusammenfassung

We study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant coordinates its ideal is generated by binomial quadrics. We present new results on the local structure of the secant variety. In particular, we show that it has rational singularities and we give a description of the singular locus. We also classify all secant varieties that are Gorenstein. Moreover, generalizing [31], we obtain analogous results for the tangential variety.

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510 Mathematik

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ISO 690MICHALEK, Mateusz, Luke OEDING, Piotr ZWIERNIK, 2015. Secant Cumulants and Toric Geometry. In: International Mathematics Research Notices (IMRN). Oxford University Press (OUP). 2015, 2015(12), pp. 4019-4063. ISSN 1073-7928. eISSN 1687-0247. Available under: doi: 10.1093/imrn/rnu056
BibTex
@article{Michalek2015Secan-52522,
  year={2015},
  doi={10.1093/imrn/rnu056},
  title={Secant Cumulants and Toric Geometry},
  number={12},
  volume={2015},
  issn={1073-7928},
  journal={International Mathematics Research Notices (IMRN)},
  pages={4019--4063},
  author={Michalek, Mateusz and Oeding, Luke and Zwiernik, Piotr}
}
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