A categorification of Galkin-Shinder's Y-F(Y) relation
Theo Raedschelders (Free University of Brussels)
Abstract: For a smooth cubic hypersurface Y, Sergey Galkin and Evgeny Shinder exhibited a relation between the naive motives of Y, the Fano variety F(Y) of lines and the Hilbert scheme Y^{[2]} of two points on Y. This relation has been shown to persist both on the level of rational Chow motives and integral Hodge structures. In a joint work with Pieter Belmans and Lie Fu, we lift this relation to derived categories by exhibiting a corresponding semi-orthogonal decomposition for the derived category of Y^{[2]}. I will explain how to obtain this semi-orthogonal decomposition from a refinement of Bondal-Orlov's results on derived categories of flips and how to further deduce an isomorphism of integral Chow motives using a recent result of Qingyuan Jiang.
algebraic geometry
Audience: researchers in the topic
Series comments: https://ed-ac-uk.zoom.us/j/89993982042
Password: a simply-connected two-dimensional variety with trivial canonical bundle (omit the space)
| Organizers: | Arend Bayer, Laure Flapan*, Emanuele Macri*, Laura Pertusi, Evgeny Shinder, Xiaolei Zhao* |
| *contact for this listing |