The moduli space of n tropically collinear points in R^d.

Título inglés	The moduli space of n tropically collinear points in Rd.
Título español	El espacio de moduli de n puntos tropicalmente colineales en Rd.
Autor/es	Develin, Mike
Organización	Amer. Inst. Math., Palo Alto (California), Estados Unidos
Revista	0010-0757
Publicación	2005, 56 (1): 1-19, 10 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	The tropical semiring (R, min, +) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of labeled n-point configurations lying on a tropical line in d-space, which is interpretable as the space of n-species phylogenetic trees. This is equivalent to the space of n x d matrices of tropical rank two, a simplicial complex. We prove that this simplicial complex is shellable for dimension d = 3 and compute is homology in this case, conjecturing that this complex is shellable in general. We also investigate the space of d x n matrices of Barvinok rank two, a subcomplex directly related to optimization, giving a complete description of this subcomplex in the case d = 3.
Clasificación UNESCO	120400
Palabras clave español	Geometría discreta ; Politopos ; Espacio de moduli ; Matrices
Código Z-Math	Zbl 1069.52014
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