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.
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