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2021 Birational geometry of moduli spaces of configurations of points on the line
Michele Bolognesi, Alex Massarenti
Algebra Number Theory 15(2): 513-544 (2021). DOI: 10.2140/ant.2021.15.513

Abstract

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.

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Michele Bolognesi. Alex Massarenti. "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

Information

Received: 20 March 2020; Revised: 4 July 2020; Accepted: 21 August 2020; Published: 2021
First available in Project Euclid: 23 June 2021

Digital Object Identifier: 10.2140/ant.2021.15.513

Subjects:
Primary: 14D22, 14H10, 14H37
Secondary: 14N05, 14N10, 14N20

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.15 • No. 2 • 2021
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