Vol. 15, No. 2, 2021

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

Michele Bolognesi and Alex Massarenti

Vol. 15 (2021), No. 2, 513–544

In this paper, we study the geometry of GIT configurations of n ordered points on 1 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
(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 Hilbert polynomial of (1)n //  PGL(2) in its natural embedding, and its automorphism group.

Mori dream spaces, moduli of curves
Mathematical Subject Classification 2010
Primary: 14D22, 14H10, 14H37
Secondary: 14N05, 14N10, 14N20
Received: 20 March 2020
Revised: 4 July 2020
Accepted: 21 August 2020
Published: 7 April 2021
Michele Bolognesi
IMAG - Université de Montpellier
Alex Massarenti
Dipartimento di Matematica e Informatica
Università di Ferrara