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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2010-08-8467 |
| Date | 2010 August 1900 |
| Creators | Buczynska, Weronika J. |
| Contributors | Sottile, Frank |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | application/pdf |
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