#### 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 ${\overline{M}}_{g,n}$. These new moduli spaces, which are modular compactifications of ${M}_{g,n}$, are related to the minimal model program for ${\overline{M}}_{g,n}$ 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 ${\overline{M}}_{g,n}$.

##### 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