Moduli Spaces of Rational Curves with Marked Points

Abstract

In the previous chapter, we have described a procedure for constructing moduli spaces of curves with marked points. These spaces are usually not compact. The key point in the understanding of the geometry of noncompact spaces is constructing their compactifications. Every noncompact space has many different compactifications, but only few of them are convenient to work with. In contrast to higher genera, the moduli space $\overline {{\mathcal {M}}_{0;n}}$ is a smooth manifold rather than orbifold. This property simplifies a bit investigation of moduli spaces in genus 0 case.