WEEKLY ACTIVITIES

Thời gian: 16h30, thứ năm, 09/05/2024

Tóm tắt: An affine algebraic variety X defined over an algebraically closed field K of characteristic zero is called flexible if the tangent space of X at any smooth point is spanned by the tangent vectors to the orbits of one-parameter unipotent group actions. It is known that if the affine cone over a smooth projective variety X with Picard rank 1 is flexible, then X is a Fano variety. Naturally, one may ask whether every Fano variety with Picard rank 1 has flexible affine cones. In dimension 2, it is proved that for every ample divisor, the affine cones over del Pezzo surfaces of degree 4 are flexible. This is also true for the affine cones over del Pezzo surface of degree at least 5. In dimension 3, the affine cones over certain families of Fano threefolds in Mori-Mukai’s classification are flexible. In dimension 4, Michael Hoff and Hoang Le Truong have shown that the affine cone over general Fano-Mukai fourfold of genus 7, 8, 9 is flexible. Moreover, the same holds for one over every Fano-Mukai fourfold of genus 7, 10. In this talk, we prove the flexibility of the affine cones over a Fano-Mukai fourfold namely the smooth complete intersection of three quadrics in P7. This talk is based on a joint work with Hoang Le Truong.

Hình thức: Offline tại phòng 612 nhà A6 hoặc online qua google meet, link cụ thể https://meet.google.com/yep-kbzk-eao?pli=1&authuser=1