Alternate Compactifications of Moduli Spaces of Curves

TL;DR

This paper surveys two interconnected research programs in the moduli of curves, focusing on classifying modular compactifications of $M_{g,n}$ and analyzing Mori chamber decompositions of $ar{M}_{g,n}$, highlighting examples and open problems.

Contribution

It provides an overview of the systematic classification of modular compactifications and the study of Mori chamber decompositions in the context of moduli spaces of curves.

Findings

Identification of key examples of compactifications

Discussion of open problems in the classification

Insights into Mori chamber decompositions

Abstract

We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classification of modular compactifications of $M_{g,n}$, and the study of Mori chamber decompositions of $\M_{g,n}$.