Constructing logarithmic moduli
In recent work, Davesh Maulik and I built a theory “logarithmic” Donaldson-Thomas invariants, and in the process we constructed a new version of the Hilbert scheme of curves: one that is sensitive to the manner in which subschemes interact with a chosen simple normal crossings divisor. There are two inputs. The first is a piece of geometry, which comes from study torus orbit closures in Hilbert schemes, following ideas of Kapranov and Tevelev. The second is an exceedingly useful piece of formalism, in the shape of tropical moduli spaces and an associated collection of Artin stacks. I’ll try to explain how to combine these ingredients to get what we get, and also share some general lessons that we learned while working this stuff out.
The synchronous discussion for Dhruv Ranganathan’s talk is taking place not in zoom-chat, but at https://tinyurl.com/2021-05-28-dr (and will be deleted after ~3-7 days).