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arXiv · 2309.05301

Classification of normal phylogenetic varieties for tripods

Rodica Andreea Dinu·Martin Vodička
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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 $G\in \{\mathbb{Z}_2, \mathbb{Z}_3, \mathbb{Z}_2\times\mathbb{Z}_2, \mathbb{Z}_4, \mathbb{Z}_5, \mathbb{Z}_7\}$.

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Rodica Andreea Dinu, Martin Vodička. 2023-09-11. Classification of normal phylogenetic varieties for tripods. https://arxiv.org/abs/2309.05301

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