English

Permutohedral complexes and rational curves with cyclic action

Algebraic Geometry 2022-10-11 v1 Combinatorics

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.

Keywords

Cite

@article{arxiv.2104.06526,
  title  = {Permutohedral complexes and rational curves with cyclic action},
  author = {Emily Clader and Chiara Damiolini and Daoji Huang and Shiyue Li and Rohini Ramadas},
  journal= {arXiv preprint arXiv:2104.06526},
  year   = {2022}
}

Comments

47 pages, 12 figures

R2 v1 2026-06-24T01:08:31.074Z