# $q$-bic Hypersurfaces

### Raymond Cheng (Columbia)

16-Jul-2021, 19:00-20:00 (12 months ago)

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 )

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 Organizer: Ravi Vakil* *contact for this listing

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