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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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Toric geometry of the 3-Kimura model for any tree

1Mathematical 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

Citation Information: Advances in Geometry. Volume 14, Issue 1, Pages 11–30, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2013-0018, January 2014

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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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