Geometry of the Kimura 3-parameter model
| dc.creator | Casanellas, Marta | |
| dc.creator | Fernandez-Sanchez, Jesus | |
| dc.date | 2007-02-27 | |
| dc.date.accessioned | 2026-07-07T07:49:21Z | |
| dc.date.available | 2026-07-07T07:49:21Z | |
| dc.description | 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. | |
| dc.description | 26 pages with 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/0702834 | |
| dc.identifier | http://arxiv.org/abs/math/0702834 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124818 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | Populations and Evolution | |
| dc.subject | 92D15;14J99;05C85 | |
| dc.title | Geometry of the Kimura 3-parameter model | |
| dc.type | text |