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The dual complex of \({\overline{M}_{0,n}}\) via phylogenetics. (English) Zbl 1342.14056

Diese kurze Note bringt einen Beweis für den folgende Satz: Der Schnitt \[ \bigcap_{i=1}^{n}\delta_{i} \] einer Menge \(\left\{\delta_{1},\dots,\delta_{n}\right\}\) Randdivisoren des Modulraums \(\overline{\mathcal{M}}_{0,n}\) stabiler Curven der Geschlecht Null mit \(n\geq3\) Punktierungen ist genau dann nicht leer, wenn die Schnitte \[ \delta_{i}\cap\delta_{j} \] für alle \(i,j\in\left\{1,\dots,n\right\}\) nicht leer sind. Über die Beweismittel sei nur in Kürze gesagt, daß sie im Spaltungsäquivalenzsatz von [Buneman, J. Comb. Theory, Ser. B 17 48–50 (1974; Zbl 0286.05102)] nach einer Umsetzung des Problems in der Theorie der phylogenetischer Bäumen besteht.

MSC:

14H10 Families, moduli of curves (algebraic)
05C05 Trees

Citations:

Zbl 0286.05102
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References:

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