Wednesday February 19th, 2025 | |
| Time: | 4:00 PM - 5:00 PM |
| Title: | Hurwitz-Brill-Noether, K3 surfaces and stability conditions |
| Speaker: | Andres Rojas, Humboldt University |
| Abstract: | |
| Brill-Noether loci for general curves are described by a collection of theorems dating back to the 70s and 80s. A remarkable proof of one of these results, the Gieseker-Petri theorem, was given by Lazarsfeld by specializing to curves on suitable K3 surfaces. This provided concrete examples of Brill-Noether general curves. On the other hand, Brill-Noether theory for curves of a fixed gonality k has not been understood until recent times, when analogues of the classic theorems have been obtained by several authors. In this talk I will explain how, by using Bridgeland stability on K3 surfaces with an elliptic pencil, one can find concrete examples of k-gonal curves which behave generically from this "Hurwitz-Brill-Noether" perspective, thus establishing a parallel to Lazarsfeld's approach. This is a joint work with G. Farkas and S. Feyzbakhsh. | |