We develop a structure theory for del Pezzo surfaces that are regular but geometrically non-normal, based on work of Reid, but now independence on the p-degree of the ground field. This leads to existence results, as well as non-existence results for ground fields of p-degree one. In turn, we settle questions arising from Koll'ar's analysis on the structure of Mori fiber spaces in dimension three. This is joint work with Andrea Fanelli.
- Algebraic Geometry Seminar