On the geometry of binary symmetric models of phylogenetic trees | Zendy

Weronika Buczyńska | Zendy; Jarosław A. Wiśniewski | Zendy

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On the geometry of binary symmetric models of phylogenetic trees

Author(s) -

Weronika Buczyńska,

Jarosław A. Wiśniewski

Publication year - 2007

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/90

Subject(s) - mathematics , geometry , binary tree , binary number , phylogenetic tree , tropical geometry , combinatorics , arithmetic , biochemistry , chemistry , gene

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.

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