Birational Geometry of moduli spaces of pointed curves

TL;DR

This thesis explores the birational geometry of moduli spaces of pointed curves, analyzing their Kodaira dimension, quotient structures, and hyperelliptic cases to advance understanding of their geometric properties.

Contribution

It synthesizes three studies on moduli spaces, providing new insights into their birational classifications, symmetry quotients, and special hyperelliptic configurations.

Findings

Determined the Kodaira dimension of certain moduli spaces

Analyzed quotient structures under subgroup actions of symmetric groups

Characterized the moduli space of hyperelliptic curves with marked points

Abstract

This is the authors doctoral thesis written at the Humboldt-University Berlin. It contains material from the three separate papers: "On the Kodaira dimension of the moduli space of nodal curves", "On quotients of $\overline{\mathcal{M}}_{g,n}$ by certain subgroups of $S_n$" and "The moduli space of hyperelliptic curves with marked points".