On phylogenetic trees - a geometer's view

Details On phylogenetic trees - a geometer's view On phylogenetic trees - a geometer's view

2006-01-14

arxiv.org/abs/math/0601357v1

Mathematics

Algebraic Geometry

44 pages, 1 figure

Scientific paper

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.

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