Abstract
In this paper we investigate properties of algebraic varieties representing group-basedphylogenetic models. We propose a method of generating many phylogenetic invariants. We provethat we obtain all invariants for any tree for the two-state Jukes-Cantor model. We conjecturethat for a large class of models our method can give all phylogenetic invariants for any tree. Weshow that for 3-Kimura our conjecture is equivalent to the conjecture of Sturmfels and Sullivant[22, Conjecture 2]. This, combined with the results in [22], would make it possible to determineall phylogenetic invariants for any tree for 3-Kimura model, and also other phylogenetic models.Next we give the (rst) examples of non-normal varieties associated to general group-based modelfor an abelian group. Following Kubjas [17] we prove that for many group-based models varietiesassociated to trees with the same number of leaves do not have to be deformation equivalent.
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