Moduli spaces in algebraic geometry

Kristin DeVleming

Moduli spaces appear as parameter spaces in algebraic geometry, where each point parameterizes a fixed type of geometric object.
They are used to classify these objects, but the spaces themselves often have interesting properties with geometric consequences, particularly when one tries to compactify them. I will introduce moduli spaces, discuss how and why one might try to compactify them, and discuss how this pertains to the “ultimate goal” of algebraic geometry: classifying all algebraic varieties.
There will be lots of pictures!