LECTURES ON
INTRODUCTION TO MODULI PROBLEMS AND ORBIT SPACES

Contents:

Preliminaries

1. The Concept of Moduli: Families / Moduli Spaces / Remarks

2. Endomorphisms of Vector Spaces: Families of Endomorphisms / Semi-Simple Endomorphisms / Cyclic Endomorphisms / Moduli and Quotients

3. Quotients: Actions of Algebraic Groups / Proof of Theorem / Affine Quotients / Linearisation / Historical Note

4. Examples: Elementary Examples / A Criterion for Stability / Binary Forms / Plane Cubics / N Ordered Points on a Line / Sequences of Linear Subspaces

5. Vector Bundles Over a Curve: Generalities and Historical Remarks / Coherent Sheaves Over X / Locally Universal Families for Semi-stable Bundles / Construction of the Quotient / Existence of a Fine Moduli Space / Proof of Theorem / Bundles Over a Singular Curve