Geodesic
On the geometry of binary symmetric models of phylogenetic trees
Journal of the European Mathematical Society, Tome 9 (2007) no. 3, pp. 609-635.

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We investigate projective varieties which are binary symmetric models of trivalent phylogenetic trees. We prove that they have Gorenstein terminal singularities and are Fano varieties of index 4 and dimension equal to the number of edges of the tree in question. Moreover any two such varieties which are of the same dimension 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-Ehrhart polynomial.
DOI : 10.4171/jems/90
Classification : 14-XX, 00-XX
Keywords: Phylogenetic tree, binary symmetric model, toric variety, Fano variety, Ehrhart polynomial, Hilbert scheme 
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Weronika Buczynska; Jaroslaw A. Wisniewski. On the geometry of binary symmetric models of phylogenetic trees. Journal of the European Mathematical Society, Tome 9 (2007) no. 3, pp. 609-635. doi : 10.4171/jems/90. http://geodesic.mathdoc.fr/articles/10.4171/jems/90/

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