Permutohedral complexes and rational curves with cyclic action

Abstract

We define a moduli space of rational curves with finite-order automorphism and weighted orbits, and we prove that the combinatorics of its boundary strata are encoded by a particular polytopal complex that also captures the algebraic structure of a complex reflection group acting on the moduli space. This generalizes the situation for Losev-Manin's moduli space of curves (whose boundary strata are encoded by the permutohedron and related to the symmetric group) as well as the situation for Batyrev-Blume's moduli space of curves with involution, and it extends that work beyond the toric context.

arXiv comment47 pages, 12 figures

References in corpus (7)

• ${\overline{M}}_{0,n}$ is not a Mori Dream Space
• Tropical curves, graph complexes, and top weight cohomology of M_g
• Some non-finitely generated Cox rings
• The automorphism group of ${\overline{M}}_{g,n}$
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• Permutohedral complexes and rational curves with cyclic action

Cited by in corpus (3)

• Permutohedral complexes and rational curves with cyclic action
• Wonderful compactifications and rational curves with cyclic action
• Intersection numbers on tropical Hassett spaces