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

## TL;DR

This paper investigates specific modular contractions of the moduli space of stable pointed curves, relating them to the minimal model program and describing their structure as log canonical models.

## Contribution

It introduces new modular compactifications of the moduli space, connecting them with the minimal model program and providing a detailed description of their boundary divisor regions.

## Key findings

- Identification of new modular compactifications
- Connection with the minimal model program
- Description of Shokurov decomposition regions

## Abstract

The aim of this paper is to study some modular contractions of the moduli space of stable pointed curves. These new moduli spaces, which are modular compactifications of the moduli space of smooth pointed curves, are related with the minimal model program for the moduli space of stable pointed curves and have been introduced in a previous work of the authors. We interpret them as log canonical models of adjoints divisors and we then describe the Shokurov decomposition of a region of boundary divisors on the moduli space of stable pointed curves.