Title: Cubic hypersurfaces: Chow groups, motives and rationality problems

Time: 10:30-11:30am, Dec. 10, 2020

Place: MCM110 & ZOOM  (Zoom ID: 466 356 2952   Password: mcm1234)

Abstract:  The Chow group of algebraic varieties is extensively used to study the rationality problem. In this talk, I will talk about two results. One is called the universal generation of the Chow groups of smooth cubic hypersurfaces. It studies the cylinder homomorphism on the Chow group by the Fano correspondence. Another is a relation of Chow motives between a smooth cubic hypersurface and its Fano variety of lines. The proof is built upon an observation due to Galkin and Shinder to study the Grothendieck ring of varieties. Besides, I will show applications of the results to integral Hodge(Tate) conjectures.