13:30 - 15:00, October 9, 2025 (Thursday) Room 515, Cosmology Building, National Taiwan University + Zoom, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Zoom)
Sections of Smooth Fibrations over $\mathbb{P}^1$ Iacopo Brivio (Harvard University)
Abstract
Let be a smooth morphism of projective complex varieties. It was shown by Pieloch, using symplectic techniques, that always has a section. I will report on work in progress with Ben Church where we present two Hodge/MMP-theoretic criteria for a fibration onto a curve to have a section. In particular, these criteria give an algebraic proof of Pieloch's result assuming the Non Vanishing Conjecture. Under a suitable ordinarity hypothesis we prove a positive characteristic version of the above results; furthermore, when this hypothesis fails, we show that there are smooth fibrations without sections.
