Toric orbifolds associated to Cartan matrices

TL;DR

This paper explores the connection between moduli stacks of pointed chains of projective lines and toric stacks derived from Cartan matrices of root systems, extending to types B and C.

Contribution

It establishes a correspondence between moduli stacks and toric stacks associated with Cartan matrices of types A, B, and C, revealing new geometric structures.

Findings

Moduli stacks coincide with certain toric stacks from Cartan matrices.

Extension of results to root systems of types B and C.

Provides a new geometric interpretation of these stacks.

Abstract

We investigate moduli stacks of pointed chains of projective lines 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.