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- Title
Automorphisms of tropical Hassett spaces.
- Authors
Freedman, Sam; Hlavinka, Joseph; Kannan, Siddarth
- Abstract
Given an integer g ≥ 0 and a weight vector w ∈ Qn ∩ (0,1)n satisfying 2g - 2 + Σ wi > 0, let Δg,w denote the moduli space of n-marked, w-stable tropical curves of genus g and volume one. We calculate the automorphism group Aut(Δg,w) for g ≥ 1 and arbitrary w, and we calculate the group Aut(Δ0,w) when w is heavy/light. In both of these cases, we show that Aut(Δg,w) ≅ Aut(Kw), where Kw is the abstract simplicial complex on {1, ..., n} whose faces are subsets with w-weight at most 1. We show that these groups are precisely the finite direct products of symmetric groups. The space Δg,w may also be identified with the dual complex of the divisor of singular curves in the algebraic Hassett space Mg,w. Following the work of Massarenti and Mella (2017) on the biregular automorphism group Aut(Mg,w), we show that Aut(Δg,w) is naturally identified with the subgroup of automorphisms which preserve the divisor of singular curves.
- Subjects
AUTOMORPHISM groups; ALGEBRAIC curves; ALGEBRAIC spaces; AUTOMORPHISMS
- Publication
Portugaliae Mathematica, 2022, Vol 79, Issue 1/2, p163
- ISSN
0032-5155
- Publication type
Article
- DOI
10.4171/PM/2075