Eduardo Esteves (IMPA)

Title: Degenerations of line bundles and divisors along curves

Abstract: A family of line bundles along a family of smooth curves parameterized by the
punctured disk can be extended in several ways over the limit stable curve of the
family. The associated divisors can each be extended in a unique way. We will discuss the
interplay between these two dynamics, part of an ongoing work to address the problem raised by
Eisenbud and Harris in the 1980’s of constructing a useful moduli of limit linear series over the
moduli of stable curves. It involves collaboration with Piere Rodríguez, Renan Santos, Eduardo Vital (IMPA)
and Omid Amini (École Polytechnique)