On generalisations of Losev-Manin moduli spaces for classical root systems

Abstract

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.

25 pages