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

TL;DR

This paper explores generalizations of Losev-Manin moduli spaces, originally associated with the root system A_n, to other classical root systems, expanding the understanding of their geometric and combinatorial structures.

Contribution

It extends the construction of Losev-Manin moduli spaces to classical root systems beyond A_n, providing new insights into their associated toric varieties.

Findings

Generalized moduli spaces for classical root systems are constructed.

Identified geometric properties of the new moduli spaces.

Connected the new spaces to existing toric variety frameworks.

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.