Toric geometry of the 3-Kimura model for any tree

Mateusz Michalek*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)11-30
Number of pages20
JournalADVANCES IN GEOMETRY
Volume14
Issue number1
DOIs
Publication statusPublished - Jan 2014
MoE publication typeA1 Journal article-refereed

Keywords

  • PHYLOGENETIC INVARIANTS
  • IDEALS
  • VARIETIES

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