On the unirationality of del Pezzo surfaces of degree 2
Event details
| Date | 25.10.2012 |
| Hour | 11:15 › 12:30 |
| Speaker | Anthony Varilly-Alvarado |
| Location | |
| Category | Conferences - Seminars |
Let k be a field and let X be a del Pezzo surface of degree at least 3 over k. By work of Segre, Manin and Koll'ar, it is known that X is k-unirational as soon as X(k) is not empty. When X is a surface of degree 2, Manin showed that if X has a k-point lying outside an explicit closed subset of X, then X is k-unirational. A close inspection of Manin's proof reveals that the explicit closed subset to be ignored is larger than originally thought. We will discuss some improvements on this closed subset and use it to show that when k is finite, all but four surfaces in characteristic 3 are provably k-unirational. One of the surfaces that eludes analysis is a nontrivial quadratic twist of the double cover of the plane ramified along the Fermat curve x4 + y4 + z4 = 0, over F_9. I will explain why the beautiful and pathological geometry of this surface make it a suitable departure point for further study on k-unirationality of del Pezzo surfaces of degree 2. This is joint work with Cecilia Salgado and Damiano Testa.
Practical information
- General public
- Free
Organizer
- CIB
Contact
- Isabelle Derivaz-Rabii