Algebraic and Arithmetic Geometry Seminar

Measuring when a line bundle on a curve is trivial

by David Holmes (Leiden)

Aula Seminari (Department of Mathematics)

Aula Seminari

Department of Mathematics

Given a family of smooth proper curves C/S and a line bundle L on C, the locus of points of S over which L is trivial is a natural invariant of the family. For applications in enumerative geometry, it is necessary to extend this construction to families  of stable (or prestable) curves. However, this ends up naturally yielding a cycle, not on S itself, but rather on a blowup of S. One can choose to push down to S, but I will try to convince the audience that, for some purposes, the cycle on the blowup is the more fundamental object. I will then describe two ways to compute the resulting class on the blowup.