Brill-Noether loci of pencils with prescribed ramification

Classical Brill-Noether theory studies projective algebraic curves through maps to projective space, using the language of linear series. A natural refinement of this framework considers linear series with prescribed ramification, leading to a deeper understanding of the geometry of curves and their maps. In this talk, I will address the problem of the existence and dimension of Brill–Noether varieties of pencils (i.e., linear series of rank one) with prescribed ramifications. I will compare this refined theory to the classical Brill–Noether problem, and present recent joint work with Andreas Leopold Knutsen, which yields new results and improves upon the previous state of the art.