On geometry of binary symmetric models of phylogenetic trees

Buczyńska, Weronika, and Wiśniewski, Jaroslaw A.. "On geometry of binary symmetric models of phylogenetic trees." Journal of the European Mathematical Society 009.3 (2007): 609-635. <http://eudml.org/doc/277731>.

@article{Buczyńska2007,
abstract = {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.},
author = {Buczyńska, Weronika, Wiśniewski, Jaroslaw A.},
journal = {Journal of the European Mathematical Society},
keywords = {phylogenetic tree; binary symmetric model; toric variety; Fano variety; Ehrhart polynomial; Hilbert scheme; toric variety; flat family; resolution; phylogenetic tree; reflexive polytope},
language = {eng},
number = {3},
pages = {609-635},
publisher = {European Mathematical Society Publishing House},
title = {On geometry of binary symmetric models of phylogenetic trees},
url = {http://eudml.org/doc/277731},
volume = {009},
year = {2007},
}

TY - JOUR
AU - Buczyńska, Weronika
AU - Wiśniewski, Jaroslaw A.
TI - On geometry of binary symmetric models of phylogenetic trees
JO - Journal of the European Mathematical Society
PY - 2007
PB - European Mathematical Society Publishing House
VL - 009
IS - 3
SP - 609
EP - 635
AB - 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.
LA - eng
KW - phylogenetic tree; binary symmetric model; toric variety; Fano variety; Ehrhart polynomial; Hilbert scheme; toric variety; flat family; resolution; phylogenetic tree; reflexive polytope
UR - http://eudml.org/doc/277731
ER -