Hilbert Schemes, Vector Bundles and Curves

Math 7800-Spring 2022

Introduction and Hartshorne Cliff Notes



Coherent Sheaves

Cohomology and Other Derived Functors

Moduli Under Construction

Constructing the Grassmannian

Constructing the Quot Scheme

Vector Bundles on Curves

Moduli of Vector Bundles on Curves

Some Archival Notes on GIT

Hilbert's 14th

Affine and Projective GIT

Numerical Criterion

Application to Vector Bundles on a Curve