On the geometry of binary symmetric models of phylogenetic trees

Autor:	Weronika Buczyńska, Jaroslaw A. Wisniewski
Rok vydání:	2007
Předmět:	Combinatorics Polynomial Hilbert scheme Applied Mathematics General Mathematics Toric variety Projective space Fano variety Geometry Fano plane Ehrhart polynomial Tree (graph theory) Mathematics
Zdroj:	Journal of the European Mathematical Society. :609-635
ISSN:	1435-9855
DOI:	10.4171/jems/90
Popis:	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.
Databáze:	OpenAIRE
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