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

TL;DR

This paper introduces a method to construct and analyze new effective curve classes on the moduli space of stable rational curves by leveraging group actions and degenerations, aiding in understanding its geometry.

Contribution

It provides a systematic approach to identify and express effective curves on , na0 using fixed loci of group actions and degeneration techniques.

Findings

Computed numerical classes of new effective curves.

Developed a strategy to express these curves as linear combinations of F-curves.

Utilized Losev-Manin spaces and toric degenerations for analysis.

Abstract

We study new effective curve classes on the moduli space of stable pointed rational curves given by the fixed loci of subgroups of the permutation group action. We compute their numerical classes and provide a strategy for writing them as effective linear combinations of F-curves, using Losev-Manin spaces and toric degeneration of curve classes.