Back to Departmental Colloquium: Spring 2021
Departmental Colloquium
Date: Tuesday, Jan 19, 2021
Time: 4:00PM
Location: JWB 335
Kristin DeVleming
University of California San Diego
Title |
Comparing compactifications of moduli spaces |
Abstract |
A foundational goal in algebraic geometry is the classification of all varieties, which are locally vanishing loci of polynomials. To make this problem tractable, one fixes discrete invariants like dimension or genus of the variety, and then studies continuous families of varieties with those invariants. The parameters for those continuous families are called moduli, and the associated parameter space is called a moduli space. Classically, there are many techniques to construct moduli spaces and compactifications of moduli spaces, from geometric invariant theory to the minimal model program, and recently there has been great progress constructing them using K-stability. I will motivate each of these techniques and ultimately focus on comparing the different results. There will be many pictures and examples! Fall 2020 |
Algebraic Geometry
Commutative Algebra
Geometry and Topology