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Algebra & Geometry Seminar

Speaker: Rikuto Ito

Affiliation: Nagoya University

Title: Arithmetic Properties of Rank-21 cubic fourfolds

Abstract: A rank-21 cubic fourfold is the cubic-fourfold analogue of an elliptic curve with complex multiplication (a CM elliptic curve). CM elliptic curves are geometrically highly symmetric, and it is classically known that they have very good arithmetic properties. We discuss how rank-21 cubic fourfolds also have good arithmetic properties, such as their fields of definition and modularity. We also introduce earlier work on the arithmetic of singular K3 surfaces, which play the role of the K3 analogue of CM elliptic curves and of rank-21 cubic fourfolds.