Heidi Goodson, Brooklyn College, City University of New York
Authors: Heidi Goodson
2023 AWM Research Symposium
Number Theory at Primarily Undergraduate Institutions [Organized by Bella Tobin and Leah Sturman]

The term 'degenerate' is used to describe abelian varieties whose Hodge rings contain exceptional cycles -- Hodge cycles that are not generated by divisor classes. We can see the effect of the exceptional cycles on the structure of an abelian variety through its Mumford-Tate group, Hodge group, and Sato-Tate group. In this talk we will examine degeneracy through these different but related lenses, specializing to Jacobians of hyperelliptic curves of the form y^2=x^m−1. We will explore the various forms of degeneracy for some examples, each illustrating different phenomena that can occur.

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