Nicola Pagani: Brill-Noether cycles on bar{M}_{g,n} I: the classes

Date: 2023-05-29

Time: 13:30 - 14:30

Zoom link:


Nicola Pagani, University of Liverpool


In the Jacobian of a smooth curve C, parametrizing line bundles of degree d, there is an interesting subvariety of codimension g-d parameterizing line bundles admittinga global section. The class of this locus admits a description as a degeneracy locus. The pullback of this class to the moduli space M_{g,n} via any of the sections of the forgetful map from the universal Jacobian J_{g,n}^d->M_{g,n} can be computed via GRR in terms of standard (tautological) classes.   In this talk we discuss how to extend these definitions and calculations to the Deligne-Mumford compactification bar{M}_{g,n}. This will involve a resolution of the section via logarithmic geometry, a new notion of “combinatorial” tautological classes on the resolution of the section, and a GRR calculation involving the latter classes. We will explain how this can be used as a procedure to produce relations in the cohomology of bar{M}_{g,n}.

A joint work in progress (Alex Abreu, Sam Molcho, Nicola Pagani).