Algebraic Curves and Moduli Spaces (Course @IST Austria, Spring 2020)

This has now evolved into an online course, if you would like to attend please contact me via email and I will send you the link to participate.

On this page you will find lecture notes and exercise sheets. If you notice any errors, please let me know.

Final Exam

I took a (virtual) Quiz as a final exam for the course, you can find the details and quiz slides here. 

Schedule

Lectures on Monday: 13:15-14:30 and Wednesday: 16:00-17:15.

Lecture Notes

Lecture-7-cohomology

Lecture-8-proper-and-affine-curves

Lecture-9-Riemann-Roch-1

Lecture-10-Dualizing-sheaf-and-theorem

Lecture-11-Curve-of-genus-zero

Lecture-12-Hurwitzs-theorem

Lecture-13-Classifying-Elliptic-curves

Lecture-14-Curves-of-genus-2-and-3

Lecture 15-Moduli functors

Lecture 16-Flat families and Hilbert scheme

Lecture 17-Hilbert schemes I

Lecture 18 More on Flatness

Lecture 19 Hilbert scheme II

Lecture 20 Grassmannians

Lecture 21 Effective Serre’s Theorem

Lecture 22-Projectivity of Hilbert scheme-1

Lecture 23-Tangent space of Hilbert scheme

Lecture 24 Not representable functors

Lecture 25-Coarse moduli space

GAGA-Theorems

 

 

Exercise sheets

Exercise Sheet 1

Exercise Sheet 2

Meta

Pages

Plain Blog Theme By NavThemes.com