Examples of Moduli Spaces

Abstract

In Sect. 6.3, we have already discussed what does the moduli space of elliptic (i.e., genus 1) curves look like. This is a rather typical example, which allows one to observe many features common for all moduli spaces. In this chapter, we will study it in more detail and consider examples of other moduli spaces. From the very beginning, we deal with moduli spaces of curves with marked points: properties of such spaces can be described “in layman’s terms” already for curves of small genus, and these properties are highly nontrivial. As the genus grows, the geometry of the moduli space becomes complicated, and a complete description of this space is usually beyond reach. Nevertheless, one can compute many important geometric characteristics of moduli spaces of curves of high genus.