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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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1615-7168
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Volume 14, Issue 1 (Jan 2014)

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Toric geometry of the 3-Kimura model for any tree

Mateusz Michałek
  • Corresponding author
  • Mathematical Institute of the Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland; Institut Fourier, Universite Joseph Fourier, 100 rue des Maths, BP 74, 38402 St Martin d’Hères, France
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Published Online: 2014-01-17 | DOI: https://doi.org/10.1515/advgeom-2013-0018

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.

About the article

Published Online: 2014-01-17

Published in Print: 2014-01-01


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2013-0018.

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Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Marta Casanellas, Jesús Fernández-Sánchez, and Mateusz Michałek
Advances in Mathematics, 2017, Volume 315, Page 285
[2]
Marie Mauhar, Joseph Rusinko, and Zoe Vernon
SIAM Journal on Discrete Mathematics, 2017, Volume 31, Number 2, Page 783
[3]
Mateusz Michałek and Emanuele Ventura
Algebra & Number Theory, 2017, Volume 11, Number 1, Page 235
[4]
Mateusz Michałek
European Journal of Combinatorics, 2017, Volume 59, Page 169
[5]
Marta Casanellas, Jesús Fernández-Sánchez, and Mateusz Michałek
Collectanea Mathematica, 2015, Volume 66, Number 2, Page 203

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