Speaker
Francesca Carocci, University of Geneva
Abstract
Basepoint-free linear series correspond to maps to projective space and thus are key to understanding the extrinsic geometry of algebraic curves.
How does a linear series degenerate when the underlying curve degenerates to a nodal curve?
Eisenbud and Harris, and Ossermann gave a satisfactory answer to this question when the nodal curve is of compact type.
In a joint work (in progress) with Luca Battistella and Jonathan Wise, we review this question from a moduli-theoretic and logarithmic perspective, which allow us to move beyond the compact type case. The logarithmic prospective sheds light on the rich combinatorial structure underlying degenerations of linear series and helps unravelling the link with the theory of matroids and Bruhat-Tits buildings.