Toric orbifolds associated to Cartan matrices

Blume, Mark

Annales de l'Institut Fourier, Tome 65 (2015) no. 2, pp. 863-901.

Nous étudions les champs de modules des chaînes de ${\mathbb{P}}^1$ marquées, reliés aux espaces de modules de Losev-Manin, et montrons que ces champs de modules coïncident avec certains champs toriques qui peuvent être décrits en termes de matrices de Cartan de systèmes de racines de type $A$. Nous considérons également les variantes de ces champs liés aux systèmes de racines de type $B$ et $C$.

We investigate moduli stacks of pointed chains of ${\mathbb{P}}^1$ related to the Losev-Manin moduli spaces and show that these moduli stacks coincide with certain toric stacks which can be described in terms of the Cartan matrices of root systems of type $A$. We also consider variants of these stacks related to root systems of type $B$ and $C$.

Classification : 14M25, 14D23, 14H10
Keywords: Losev-Manin moduli spaces, toric stacks, root systems, Cartan matrices, permutohedron.
Mot clés : Espaces de modules de Losev-Manin, champs toriques, systèmes de racines, matrices de Cartan, permutoèdre.

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