Smooth projective fibrations over the projective line and their sections
2025-01-31 12:00 - 13:00 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Iacopo Brivio
Title: Smooth projective fibrations over the projective line and their sections
Abstract: Suppose $fcolon Xto mathbf{CP}^1$ is a smooth projective fibration, is it then true that $f$ has a section? This deceptively simple result was established by Seidel and McDuff using deep methods of symplectic geometry. Alex Pieloch recently generalized this to morphisms with at most one singular fibers and furthermore showed that $X$ uniruled, that is covered by images of $mathbf{P}^1$. In my talk I will explain how to recover Pieloch’s result from the Good Minimal Model Conjecture.
