Classifying Possible Density Degree Sets for Hyperelliptic Curves
Abstract: Let C be a smooth, projective, geometrically integral hyperelliptic curve of genus g → 2 over a number field k. To study the distribution of degree d points on C, we introduce the notion of P1- and AV-parameterized points, which arise from natural geometric constructions. These provide a framework for classifying density degree sets, an important invariant of a curve that records the degrees d for which the set of degree d points on C is Zariski dense. Zariski density has two geometric sources: If C is a degree d cover of P1 or an elliptic curve E of positive rank, then pulling back rational points on P1 or E give an infinite family of degree d points on C. Building on this perspective, we give a classification of the possible density degree sets of hyperelliptic curves.
Event Type: Dissertation. Research Area: Mathematics. Speaker Name: Jasmine Camero. Speaker Institution: Emory University. Speaker Website: https://scholarblogs.emory.edu/math/files/2025/12/Camero-Dissertation-Announcement.pdf.
Thursday, March 5, 2026, 4:00 PM – 5:00 PM.
White Hall 103.
For more info visit scholarblogs.emory.edu.