Abstract:

I will explain the matrix local equations defining the moduli spaces of stable maps of arbitrary genus, found jointly by Jun Li and the speaker. These equations already guided us to find explicit global resolutions for these moduli spaces in the cases when the genera are one and two. By Murphy’s law, stable map moduli possess arbitrary singularities. Turning to this, I will explain Lafforgue’s version of Mnev’s universality, how it leads to standard local equations for arbitrary singularity types, and how it should guide to resolve arbitrary singularities.