Gorenstein property for phylogenetic trivalent trees

We study the Gorenstein property for phylogenetic group-based models. We prove that the varieties associated to a trivalent tree and any of the groups Z3 and Z2×Z2 are Gorenstein Fano varieties, extending the results of Buczyńska and Wiśniewski for the group Z2.

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Bibliographic Details
Published in:Journal of algebra 2021-06, Vol.575, p.233-255
Main Authors: Dinu, Rodica, Vodička, Martin
Format: Article
Language:English
Subjects:
Fano variety
Gorenstein polytope
Group-based model
Phylogenetic trivalent tree
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Description
Summary:We study the Gorenstein property for phylogenetic group-based models. We prove that the varieties associated to a trivalent tree and any of the groups Z3 and Z2×Z2 are Gorenstein Fano varieties, extending the results of Buczyńska and Wiśniewski for the group Z2.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2021.02.012