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Losev and Manin introduced fine moduli spaces $\bar{L}_n$ of stable $n$-pointed chains of projective lines. The moduli space $\bar{L}_{n+1}$ is isomorphic to the toric variety $X(A_n)$ associated with the root system $A_n$, which is part of a general construction to associate with a root system $R$ of rank $n$ an $n$-dimensional smooth projective toric variety $X(R)$. In this paper we investigate generalisations of the Losev-Manin moduli spaces for the other families of classical root systems.

On Generalisations of Losev-Manin Moduli Spaces for Classical Root Systems