# On geometry of binary symmetric models of phylogenetic trees

Weronika Buczyńska; Jaroslaw A. Wiśniewski

Journal of the European Mathematical Society (2007)

- Volume: 009, Issue: 3, page 609-635
- ISSN: 1435-9855

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topBuczyńska, 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 -

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