In this paper, we study the geometry of GIT configurations of ordered points on both from the birational and the biregular viewpoint. In particular, we prove that any extremal ray of the Mori cone of effective curves of the quotient// , 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 Hilbert polynomial of // in its natural embedding, and its automorphism group.
"Birational geometry of moduli spaces of configurations of points on the line." Algebra Number Theory 15 (2) 513 - 544, 2021. https://doi.org/10.2140/ant.2021.15.513