An extremal effective survey about extremal effective cycles in moduli spaces of curves

TL;DR

This paper surveys recent progress and unresolved questions regarding extremal effective divisors and cycles in the moduli spaces of algebraic curves, highlighting key developments and open problems.

Contribution

It provides a comprehensive overview of the current state and challenges in understanding extremal effective cycles in moduli spaces of curves.

Findings

Summarizes recent advances in extremal effective divisors

Identifies open problems in higher codimension cycles

Highlights key techniques used in the field

Abstract

We survey recent developments and open problems about extremal effective divisors and higher codimension cycles in moduli spaces of curves.