SFU NTAG Seminar: Graham McDonald

Let $A$ be an abelian surface. We investigate curves in a linear system on the dual abelian surface $\hat{A}$. There is an isomorphism of moduli spaces due to Yoshioka between the space $K_3(A)$ parametrizing 0-dimensional length-4 subschemes on $A$ that sum to the identity in the group law, and the space $K_{\hat{A}}(0,\hat{\ell},-1)$ parametrizing certain rank 1 torsion free sheaves supported on curves in a linear system on $\hat{A}$. Leveraging this isomorphism together with quadratic forms associated to symmetric line bundles on $A$, we develop a computational method that allows us to characterize the singularities of the curves that correspond to a finite distinguished subset of $K_3(A)$. In this talk we will describe these methods and compute an example of a curve with two nodal singularities.

This is joint work with Katrina Honigs and Peter McDonald.