Geometry of the Kimura 3-parameter model

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The Kimura 3-parameter model on a tree of n leaves is one of the most used in phylogenetics. The affine algebraic variety W associated to it is a toric variety. We study its geometry and we prove that it is isomorphic to a geometric quotient of the affine space by a finite group acting on it. As a consequence, we are able to study the singularities of W and prove that the biologically meaningful points are smooth points. Then we give an algorithm for constructing a set of minimal generators of the localized ideal at these points, for an arbitrary number of leaves n. This leads to a major improvement of phylogenetic reconstruction methods based on algebraic geometry.
26 pages with 4 figures

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Algebraic Geometry, Commutative Algebra, Populations and Evolution, 92D15;14J99;05C85

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http://salesiana.dossiersoluciones.com/handle/123456789/124818

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702834
 http://arxiv.org/abs/math/0702834

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arXiv