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

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 ${\overline{M}}_{g,n}$.