Tautological Classes on the Moduli Spaces of Stable Maps to P r via Torus Actions

@inproceedings{Oprea2005TautologicalCO,
  title={Tautological Classes on the Moduli Spaces of Stable Maps to P r via Torus Actions},
  author={Dragos Oprea},
  year={2005}
}
We present a localization proof of the fact that the cohomology of the moduli spaces of genus zero stable maps to projective spaces is entirely tautological. In addition, we obtain a description of a Bialynicki-Birula decomposition of the stack of stable maps in the context of Gathmann’s moduli spaces of maps with prescribed contact order to a fixed hyperplane. We show that the decomposition is filterable.