Description
Title: Fourier-Mukai transforms and log geometry.
Abstract:
I will review progress in our understanding of the intersection theory of degenerating families of abelian schemes, namely the compactified Jacobians and Mumford's canonical partial compactification of the moduli space of principally polarized abelian varieties, parametrizing degenerations of torus rank at most one. I will state the main results and attempt to explain our approach to these problems, which combines Arinkin's perspective on how Mukai's derived autoequivalence of the derived category of a ppav degenerates with the logarithmic resolutions of the fundamental geometric structures enjoyed by an abelian scheme. The talk will be based on joint work with Bae-Pixton and joint work in progress with Bae-Feusi-Iribar Lopez.