Full Record

Author | Buczynska, Weronika J. |

Title | Phylogenetic Toric Varieties on Graphs |

URL | http://hdl.handle.net/1969.1/ETD-TAMU-2010-08-8467 |

Publication Date | 2010 |

Date Available | 2010-10-14 16:08:08 |

Date Accessioned | 2010-10-14 16:08:08 |

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 | 2017-09-05 |

Date Indexed | 2017-09-06 |

Issued Date | 2010-10-12 00:00:00 |