Year: 2006
Type: preprint
Abstract: We investigate projective varieties which are geometric models of binary symmetric phylogenetic 3-valent trees. We prove that these varieties have Gorenstein terminal singularities (with small resolution) and they are Fano varieties of index 4. Moreover any two such varieties associated to trees with the same number of leaves 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-Ehrhard polynomial.
Source: arXiv (Cornell University)
Institution: University of Warsaw
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W19390597