On smooth cylindrical rational Fano fourfolds
Người báo cáo: Nguyễn Thị Ánh Hằng

Thời gian: 15:00 - 16:00, October 19, 2021

Tham gia bằng Google Meet: meet.google.com/oqm-weaf-cos

Tóm tắt: A smooth complex projective variety $X$ is called {it cylindrical} if it contains a cylinder, that is, a principal Zariski open subset $U$ isomorphic to a product $Z times mathbb A^1$, where $Z$ is a variety and $mathbb A^1$ is the affine line over $mathbb C$. The main goal of this talk is to study the existence of a cylinder in some certain classes of Mukai fourfolds of genus $6, 7, 8, 9$. More precisely, we construct new families of smooth Fano fourfolds with Picard rank $1$ which contain open $mathbb A^1$-cylinders. In particular, we show that every Mukai fourfold of genus $8$ is cylindrical and there exists a family of cylindrical Gushel-Mukai fourfolds. This is a joint work with H. L. Truong and M. Hoff.

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