Low degree equations for phylogenetic group-based models

• Autores: Marta Casanellas Rius , Jesús Fernández Sánchez , Mateusz Michalek
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 66, Fasc. 2, 2015, págs. 203-225
• Idioma: inglés
• DOI: 10.1007/s13348-014-0120-0
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• Resumen

  • Motivated by phylogenetics, our aim is to obtain a system of low degree equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group G, we provide an explicit construction of {{\mathrm{codim}}}X polynomial equations (phylogenetic invariants) of degree at most |G| that define the variety X on a Zariski open set U. The set U contains all biologically meaningful points when G is the group of the Kimura 3-parameter model. In particular, our main result confirms (Michałek, Toric varieties: phylogenetics and derived categories, PhD thesis, Conjecture 7.9, 2012) and, on the set U, Conjectures 29 and 30 of Sturmfels and Sullivant (J Comput Biol 12:204–228, 2005).

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