Log canonical models for $\bar{M}_{g,n}$

TL;DR

This paper derives a unified formula for log canonical models of the moduli space of pointed stable curves, extending previous genus-zero results to all genera, and encompasses Hassett's weighted pointed stable curves.

Contribution

It provides a comprehensive formula for log canonical models of ar{M}_{g,n}, generalizing earlier genus-zero findings to all genera and unifying various Hassett moduli spaces.

Findings

Unified formula for log canonical models of ar{M}_{g,n}

Extension of genus-zero results to all genera

Inclusion of Hassett's weighted moduli spaces

Abstract

We prove a formula of log canonical models for moduli space $\bar{M}_{g,n}$ of pointed stable curves which describes all Hassett's moduli spaces of weighted pointed stable curves in a single equation. This is a generalization of the preceding result for genus zero to all genera.