Vol. 15, No. 5, 2021

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On some modular contractions of the moduli space of stable pointed curves

Giulio Codogni, Luca Tasin and Filippo Viviani

Vol. 15 (2021), No. 5, 1245–1281
Abstract

The aim of this paper is to study some modular contractions of the moduli space of stable pointed curves M¯g,n. These new moduli spaces, which are modular compactifications of Mg,n, are related to the minimal model program for M¯g,n and have been introduced by Codogni et al. (2018). We interpret them as log canonical models of adjoint divisors and we then describe the Shokurov decomposition of a region of boundary divisors on M¯g,n.

Keywords
moduli of curves, birational contractions, modular compactifications
Mathematical Subject Classification 2010
Primary: 14H10
Secondary: 14D22, 14D23, 14E30
Milestones
Received: 7 March 2020
Revised: 17 August 2020
Accepted: 9 November 2020
Published: 30 June 2021
Authors
Giulio Codogni
Dipartimento di Matematica
Università degli Studi di Roma Tor Vergata
Roma
Italy
Luca Tasin
Dipartimento di Matematica F. Enriques
Università degli Studi di Milano
Milano
Italy
Filippo Viviani
Dipartimento di Matematica e Fisica
Università degli Studi Roma Tre
Rome
Italy