2014/02/27 by Marta Casanellas, Casanellas, Marta, Jesús Fernández-Sánchez +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #13P25 #14Q99 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Biological sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation #Populations and Evolution (q-bio.PE) #math.AG #msc:13P25 #msc:14Q99 #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1402.6945
22 pages, 7 figures
arxiv created 2014/02/27 · openalex publication_date 2014/02/27 · arxiv updated 2014/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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 codim X 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.