Marta Casanellas, Jesús Fernández-Sánchez, Mateusz Michałek
(Submitted on 27 Feb 2014)
Motivated by phylogenetics, our aim is to obtain a system of 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 codimX phylogenetic invariants (polynomial equations) 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 a conjecture by the third author and, on the set U, a couple of conjectures by Bernd Sturmfels and Seth Sullivant.