Explicit Kummer varieties of hyperelliptic curves

Abstract: I will report on work with Jack Thorne in which we study Kummer varieties of odd hyperelliptic curves using the theory of pure spinors for SO_{2g+1}. This provides an explicit description of these Kummers, which is suitable to study heights of rational points, generalising the works of Cassels--Flynn and Stoll to arbitrary genus. I will also give some consequences to arithmetic statistics.

number theory

Audience: researchers in the topic

London number theory seminar

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