Abstract

Consider a conic bundle over a smooth incomplete curve C, i.e. a smooth surface S with a proper surjective morphism to C such that the push-forward of the structure sheaf of S coincides with the structure sheaf of C, and the anticanonical class of S is ample over C. If the base field is perfect, a conic bundle always extends to a conic bundle over a completion of C. I will tell about a necessary and sufficient condition for the existence of such an extension in the case of an arbitrary base field. The talk is based on a joint work in progress with V.Vologodsky.

Speaker

Konstantin Shramov has been at HSE University since 2010. His professional interests are Birational geometry, Fano varieties, minimal model program, log-canonical thresholds, Kahler-Einstein metrics, Cremona group, birational rigidity.

个人主页：

https://www.hse.ru/en/org/persons/26335794