Speaker: Montserrat Teixidor (Tufts University)

Title: Brill-Noether loci

Abstract:

Brill-Noether loci are defined as the set of curves of genus g that have an unexpected linear series of degree d and dimension r.

Pflueger showed that these loci are non-empty when the expected codimension is at most g-3. By studying linear series on chains of elliptic curves, we give a new proof of a slightly refined version of this result. We can also look at the behavior of the generic curve in the locus.

An interesting conjecture of Auel and Haburcak states that these loci are distinct and not contained in each other, unless they come from adding or removing fixed points. Their proof made use of curves contained in K3 surfaces and was sufficient to prove the result in small genus. Using chains of elliptic curves, we can obtain additional information.