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ON THE FIRST STEPS OF THE MINIMAL MODEL PROGRAM FOR THE MODULI SPACE OF STABLE POINTED CURVES

Part of: Curves Families, fibrations Birational geometry

Published online by Cambridge University Press:  22 April 2021

Giulio Codogni ,
Luca Tasin  and
Filippo Viviani Open the ORCID record for Filippo Viviani [Opens in a new window]
Giulio Codogni
Affiliation:
Dipartimento di Matematica, Università Tor Vergata, Via della Ricerca Scientica 1, 00133 Roma, Italy (codogni@mat.uniroma2.it)
Luca Tasin
Affiliation:
Dipartimento di Matematica F. Enriques, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy (luca.tasin@unimi.it)
Filippo Viviani
Affiliation:
Dipartimento di Matematica, Università Tor Vergata, Via della Ricerca Scientica 1, 00133 Roma, Italy (codogni@mat.uniroma2.it) Dipartimento di Matematica e Fisica, Università Roma Tre, 00146 Roma, Italy (viviani@mat.uniroma3.it)
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Abstract

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The aim of this paper is to study all the natural first steps of the minimal model program for the moduli space of stable pointed curves. We prove that they admit a modular interpretation, and we study their geometric properties. As a particular case, we recover the first few Hassett–Keel log canonical models. As a by-product, we produce many birational morphisms from the moduli space of stable pointed curves to alternative modular projective compactifications of the moduli space of pointed curves.

Keywords

Minimal model programmoduli space of curvesmodular compactifications

MSC classification

Primary: 14H10: Families, moduli (algebraic)
Secondary: 14E30: Minimal model program (Mori theory, extremal rays) 14D23: Stacks and moduli problems 14H20: Singularities, local rings
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 1 , January 2023 , pp. 145 - 211
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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