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
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 , . 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  on the degree in which the ideal associated to the 3-Kimura model is generated on that set.
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