Math 788 -- Linear systems and positivity of vector bundles -- Spring 2024

This is an advanced topics course on linear systems, line bundles, and vector bundles in algebraic geometry. Our goal is to study how we use these objects to encode geometric information.

Lecture: Tuesday and Thursday 2:30-3:45 PM in MSC W303

Instructor: Brooke Ullery (bullery@emory, office MSC E416)

Office hours (subject to change):

Thursday 1:30-2:30 PM (in MSC E416)
Wednesday 1:30-2:30 (on Zoom)

Text: Lazarsfeld's "Positivity in Algebraic Geometry" books I and II would be useful to have, but are definitely not required.

Homework: I will occasionally assign exercises of varying difficulty throughout lecture. I'll also record them below.

Grading: To receive an A in the class, you should hand in complete solutions to three exercises throughout the semester and actively engage with the material in office hours or in class. To receive an A-, you should submit solutions to two exercises and attend class regularly.

Schedule

Here I'll post the topics we cover each day of lecture, the corresponding lecture notes (once we finish that section), and any assigned homework problems. Keep in mind the lecture notes from one class may not be posted until after the following class if we stop in the middle of a section.

Date Topics covered Homework Comments

Thursday 1/18

Tuesday 1/23

Thursday 1/25