【114/10/17】13:00-14:00 Dr. Iacopo Brivio (Harvard University)
發佈日期 :
2025-10-14
| Geometry Seminar | |
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| Time | 2025-10-17 13:00-14:00 |
| Venue | 數學館2樓3175教室 |
| Speaker | Dr. Iacopo Brivio (Harvard University) |
| Title | Sections of Smooth Fibrations over $\mathbb{P}^1$ |
| Abstract | Let $f\colon X\to\mathbb{P}^1$ be a smooth morphism of projective complex varieties. It was shown by Pieloch, using symplectic techniques, that $f$ 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 Abundance 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 $X\to\mathbb{P}^1$ without sections. |
| Organizer | 賴青瑞 |
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