Wall-crossing for Calabi-Yau fourfolds and applications

Abstract: There are multiple existing theories studying wall-crossing of sheaf-counting invariants in dimensions less than or equal to three. Recently these invariants were also extended to Calabi-Yau fourfolds where it was reasonable to ask about an analogous story. I will explain the framework leading to the wall-crossing formulae proposed by Joyce and describe their proof. The main goal of this project is the proof of existing conjectures relating different stable pairs counting points, curves and surfaces in Calabi-Yau fourfolds. For example, it proves my previous computations for Hilbert schemes of points.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar