#### 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