Log liftability to characteristic zero of F-split surfaces
Given a projective variety X over an algebraically closed field of characteristic p>0, it is an interesting question to know whether it admits a lifting to characteristic zero.
This is false in general (the first examples have been constructed in the sixties), but understanding the possible obstructions or constructing new examples is still an active area of research.
In the first 30 minutes, I will recall some of the previous results on liftability for smooth projective varieties and I will try to build some intuition on lifting to characteristic zero.
In the research part, I will discuss a work in progress with I. Brivio, T. Kawakami and J. Witaszek, where we show that globally F-split surfaces (which can be thought as arithmetically well-behaved log Calabi-Yau pairs) are log liftable to characteristic zero.
As a corollary we deduce the Bogomolov bound on the number of singular points of F-split klt del Pezzo surfaces (which was known to be false without the $F$-splitness condition).
- Informed public
- Zsolt Patakfalvi
- Monique Kiener (if you want to attend to the seminar by zoom, please contact me, and I'll give you the link)