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Title Phylogenetic Toric Varieties on Graphs
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Publication Date
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University/Publisher Texas A&M University
Abstract We define the phylogenetic model of a trivalent graph as a generalization of a binary symmetric model of a trivalent phylogenetic tree. If the underlining graph is a tree, the model has a parametrization that can be expressed in terms of the tree. The model is always a polarized projective toric variety. Equivalently, it is a projective spectrum of a semigroup ring. We describe explicitly the generators of this projective coordinate ring for graphs with at most one cycle. We prove that 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, which uses the structure of the graph as a sum of elementary ones. Also, this Hilbert function of phylogenetic model of a graph with g cycles is meaningful for the theory of connections on a Riemann surface of genus g.
Subjects/Keywords toric variety; phylogenetics; Hilbert function
Contributors Sottile, Frank (advisor); Dos-Reis, Gabriel (committee member); Lima-Filho, Paulo (committee member); Matusevich, Laura F. (committee member)
Language en
Country of Publication us
Record ID handle:1969.1/ETD-TAMU-2010-08-8467
Repository tamu
Date Retrieved
Date Indexed 2017-09-06
Issued Date 2010-10-12 00:00:00

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