Algebraic Geometry Seminar: "On the Chow ring structure of the cubic hypersurface"
Humberto Diaz, University of California, Riverside
Abstract: In this talk, I will discuss the Chow ring structure of a hypersurface of degree 3 in projective space. The total Chow ring of a hypersurface of degree greater than 2 (say, over the complex numbers) is infinite rank by (generalizations of) Mumford’s theorem and is quite mysterious in general. On the other hand, for cubic hypersurfaces, we show that the Chow ring structure is as simple as possible; namely, the intersection of any two positive dimensional cycles is proportional to the class of a linear section. The proof is elementary and relies on a beautiful relation, established by Galkin and Shinder, between the cubic hypersurface and its Fano variety of lines.
Host: Matt Kerr