Birational geometry of 3-fold conic bundles

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，Jia Jia 贾甲

Speaker：

Vyacheslav V. Shokurov

Steklov Mathematical Institute of Russian Academy

Time：

Fri., 15:30-16:30, July 11, 2025

Venue：

B725, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Birational geometry of 3-fold conic bundles

It will be a survey of current results and state of birational geometry for conic bundles in dimension 3. In particular, we discuss the invariant |2K+C| where K are canonical and discriminant divisors respectively on the base surface of a standard 3-fold conic bundle. The main result here (with Prokhorov) is the invariance of dim|2K+C|, that is, its independence on a conic bundle structure of a 3-fold, modulo birationally bounded set of 3-folds.

About the speaker

Vyacheslav Shokurov is a Russian mathematician best known for his research in algebraic geometry. The proof of the Noether–Enriques–Petri theorem, the cone theorem, the existence of a line on smooth Fano varieties and, finally, the existence of log flips—these are several of Shokurov's contributions to the subject.