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We study new effective curve classes on the moduli space of stable pointedrational curves given by the fixed loci of subgroups of the permutation groupaction. We compute their numerical classes and provide a strategy for writingthem as effective linear combinations of F-curves, using Losev-Manin spaces andtoric degeneration of curve classes.

Effective curves on $\overline{M}_{0,n}$ from group actions