$q$-bic Hypersurfaces

Abstract: Let’s count: 1, $q$, $q+1$; here, $q$ is a power of a prime $p$. In this talk, I will sketch an analogy between the geometry of a class of hypersurfaces over a field of positive characteristic $p$, which I call $q$-bic hypersurfaces, and the geometry of low degree hypersurfaces, such as quadrics and cubics, over the complex numbers. For instance, a smooth $q$-bic threefold has a smooth Fano surface of lines, and the intermediate Jacobian of the threefold is isogenous to the Albanese of the Fano surface.

algebraic geometry

Audience: researchers in the topic

( slides | video )

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com