Speaker: Eric Zaslow (Northwestern University)
Title: New Counts of Nodal Curves
Abstract: I will describe work in progress falling somewhere between the count of nodal curves on K3 and Kontsevich’s famous count of rational plane curves of degree d meeting 3d-1 points. Specifically, I will try to count nodal curves in a toric Fano surface with fixed intersection with the toric boundary. In the case of P^2, this means genus-zero degree-d curves fixing 3d points along the three coordinate axes. While I can’t give a general formula (yet?), I can give a definition and present a couple of interesting (to me) ways that use a kind of mirror duality to approach the computation. Results agree (so far) for low degrees in many examples. This work is joint with Mingyuan Hu and Tom Graber.