Birational geometry of moduli spaces of configurations of points on the line

@article{Bolognesi2017BirationalGO,
  title={Birational geometry of moduli spaces of configurations of points on the line},
  author={M. Bolognesi and Alex Massarenti},
  journal={arXiv: Algebraic Geometry},
  year={2017}
}
In this paper we study the geometry of GIT configurations of $n$ ordered points on $\mathbb{P}^1$ both from the the birational and the biregular viewpoint. In particular, we prove that any extremal ray of the Mori cone of effective curves of the quotient $(\mathbb{P}^1)^n//PGL(2)$, taken with the symmetric polarization, is generated by a one dimensional boundary stratum of the moduli space. Furthermore, we develop some technical machinery that we use to compute the canonical divisor and the… Expand
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