n Bertram 0.1. Introduction to Moduli Spaces. Moduli in algebraic geometry refers to the continuous variation of geometric objects that are bundled in families, and a moduli space is a …

Last time we discussed the example of the moduli functor of families of vector spaces of rank n. In the following two lectures, we will take a step back and discuss the general formalism of …

Their moduli are denoted Ag, Ag;N, Ag;N;d and Sh(G; X). The latter is called a PEL-Shimura variety (polarization, endomorphism, level structure). The Ag;N;d are critical in Falting's proof …

1.1 Motivating examples Before diving in, I want to give some motivating examples of works that crucially relied on the tools and techniques of moduli theory. Many of the moduli theoretic …

But for now, we will look at G(k; n), the Grassmanian, which we will use to study Chow Varieties G(k; d; n), which will be used to construct M0;n, the moduli space of n-pointed stable curves of …

In this course, I would like to present the basic ideas and formalism underlying the concept of moduli space, along with some main examples of interdisciplinary interest.

It’s a learning note for moduli problems of vector bundles. The main reference for moduli space and geometric invariant theory is [Hos16], and the main refer-ence for algebraic stack is [Hei10].