Positivity in Algebraic Geometry
Resources
We are reading Positivity in Algebraic Geometry I by Robert Lazarsfeld. The current plan is to cover Chapter 1 (Ample and Nef Bundles) and Chapter 2 (Linear Series) very thoroughly, and then use this foundation to cover some important consequences: the Lefschetz hyperplane theorem and the Kodaira vanishing theorem. If you’d like to be kept updated, please join the mailing list.
Schedule
| Date | Speaker | Reading |
|---|---|---|
| Week 1 (February 8) | John Cobb | 1.1 Preliminaries: Divisors, Line Bundles, and Linear Series (17 pages) |
| Week 2 (February 15) | Alex Hof | 1.2-3 The Classical Theory, \(\mathbb{Q}\)-Divisors and \(\mathbb{R}\)-Divisors (26 pages) |
| Week 3 (February 22) | Colin | 1.4 Nef Line Bundles and Divisors (20 pages) |
| March 4 (March 1) | Lazarsfeld | Pythagorean triples and parametrized curves |
| Week 5 (March 22) | Asvin | 1.5 Examples and Complements (18 pages) |
| Week 6 (March 29) | Ivan | 1.8 Castelnuovo-Mumford Regularity (21 pages) |
| Week 7 (April 5) | Yifan | 2.1 Asymptotic Theory (18 pages) |
| Week 8 (April 12) | John Cobb | 2.2 Big Line Bundles and Divisors (18 pages) |
| Week 9 (April 19) | Daniel Erman (online!) | 2.3 Examples and Complements (15 pages) |
| Week 10 (April 26) | Colin | 4.1-3 Kodaira and Nakano Vanishing Theorems (21 pages) |
I’m leaving some room to split any readings into two weeks, or to veer in another direction if we would like. I know that Daniel Erman would like to give a lecture. By coincidence, Lazarsfeld will be in town around the middle of the semester.
Meeting Structure
We will be meeting weekly at 4:00-5:00 on Tuesdays in Van Vleck B231. While reading, write any questions you have and bring them. Each week the speaker will be giving a ~50 minute talk summarizing and motivating the reading that week, preferably picking a few of the many examples to work through in detail. Note that being the speaker does not mean you are expected to know everything – You can have lots of questions too. During the talk, you should ask your questions for everyone to collectively discuss, perhaps saving any “harder” questions for the end.