Classification of normal phylogenetic varieties for tripods

Author:

Rodica Andreea Dinu, Martin Vodička

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Combinatorics (math.CO)

journal:

date:

2023-09-10 16:00:00

Abstract

We provide a complete classification of normal phylogenetic varieties coming from tripods, and more generally, from trivalent trees. Let $G$ be an abelian group. We prove that the group-based phylogenetic variety $X_{G,\mathcal{T}}$, for any trivalent tree $\mathcal{T}$, is projectively normal if and only if $G\in \{\mathbb{Z}_2, \mathbb{Z}_3, \mathbb{Z}_2\times\mathbb{Z}_2, \mathbb{Z}_4, \mathbb{Z}_5, \mathbb{Z}_7\}$.

PDF: Classification of normal phylogenetic varieties for tripods.pdf