Given an integer and a weight vector satisfying , let denote the moduli space of -marked, -stable tropical curves of genus and volume one. We calculate the automorphism group for and arbitrary , and we calculate the group when is heavy/light. In both of these cases, we show that , where is the abstract simplicial complex on whose faces are subsets with -weight at most 1. We show that these groups are precisely the finite direct products of symmetric groups. The space may also be identified with the dual complex of the divisor of singular curves in the algebraic Hassett space . Following the work of Massarenti and Mella (2017) on the biregular automorphism group , we show that is naturally identified with the subgroup of automorphisms which preserve the divisor of singular curves.
Cite this article
Sam Freedman, Joseph Hlavinka, Siddarth Kannan, Automorphisms of tropical Hassett spaces. Port. Math. 79 (2022), no. 1/2, pp. 163–197DOI 10.4171/PM/2075