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Toric geometry of the 3-Kimura model for any tree

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2014

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https://doi.org/10.1515/advgeom-2013-0018
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Advances in Geometry. De Gruyter. 2014, 14(1), pp. 11-30. ISSN 1615-715X. eISSN 1615-7168. Available under: doi: 10.1515/advgeom-2013-0018

Zusammenfassung

In this paper we present geometric features of group-based phylogenetic models. We address a long standing problem of determining the ideal of the claw tree [23], [12]. We focus on the 3-Kimura model. In particular we present a precise geometric description of the variety associated to any tree on a Zariski open set. This set contains all biologically meaningful points. The result confirms the conjecture of Sturmfels and Sullivant [23] on the degree in which the ideal associated to the 3-Kimura model is generated on that set.

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ISO 690MICHALEK, Mateusz, 2014. Toric geometry of the 3-Kimura model for any tree. In: Advances in Geometry. De Gruyter. 2014, 14(1), pp. 11-30. ISSN 1615-715X. eISSN 1615-7168. Available under: doi: 10.1515/advgeom-2013-0018
BibTex
@article{Michalek2014Toric-52537,
  year={2014},
  doi={10.1515/advgeom-2013-0018},
  title={Toric geometry of the 3-Kimura model for any tree},
  number={1},
  volume={14},
  issn={1615-715X},
  journal={Advances in Geometry},
  pages={11--30},
  author={Michalek, Mateusz}
}
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