Journal of Algebraic Combinatorics

, Volume 35, Issue 3, pp 421-460

First online:

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Phylogenetic toric varieties on graphs

  • Weronika BuczyńskaAffiliated withDepartment of Mathematics, Texas A&M University Email author 


We define phylogenetic projective toric model of a trivalent graph as a generalization of a binary symmetric model of a trivalent phylogenetic tree. Generators of the projective coordinate ring of the models of graphs with one cycle are explicitly described. The phylogenetic models of graphs with the same topological invariants are deformation-equivalent and share the same Hilbert function. We also provide an algorithm to compute the Hilbert function.


Binary symmetric model GIT quotient Hilbert function