Degeneracy and Sato-Tate Groups in Dimension Greater than 3
Heidi Goodson (Brooklyn College (CUNY))
29-Nov-2022, 21:00-22:00 (17 months ago)
Abstract: 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 I will discuss degeneracy through these different but related lenses, specializing to Jacobians of hyperelliptic curves of the form $y^2=x^m−1$. Together, we will explore the various forms of degeneracy for several examples, each illustrating different phenomena that can occur.
number theory
Audience: researchers in the topic
University of Arizona Algebra and Number Theory Seminar
Organizers: | Aparna Upadhyay*, Pan Yan* |
*contact for this listing |
Export talk to