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math.NT2026
Likely and unlikely ramification of algebraic points on curves
Bianca Viray, Isabel Vogt
This paper initiates the study of arithmetic properties of closed points of arbitrary degree on curves. We show that a pointless curve of rank can have only finitely many cycli…
math.AG2026
Recent advances in Brill--Noether theory and the geometry of Brill--Noether curves
Isabel Vogt
The first goal of this article is to survey recent progress in Brill--Noether theory, including both the study of the moduli space of maps from a curve to projective space and the…