On phylogenetic trees - a geometer's view

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We investigate projective varieties which are geometric models of binary symmetric phylogenetic 3-valent trees. We prove that these varieties have Gorenstein terminal singularities (with small resolution) and they are Fano varieties of index 4. Moreover any two such varieties associated to trees with the same number of leaves are deformation equivalent, that is, they are in the same connected component of the Hilbert scheme of the projective space. As an application we provide a simple formula for computing their Hilbert-Ehrhard polynomial.
44 pages, 1 figure

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Algebraic Geometry, Populations and Evolution, 14M25 (primary) 14J45, 92B10 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/107553

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0601357
 http://arxiv.org/abs/math/0601357

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arXiv