Moduli spaces are fundamental objects in algebraic geometry. They provide solutions to classification problems. There are invariants attached to these moduli spaces, such as Poinca're polynomials, which help to better understand them, and others, such as Donaldson-Thomas invariants, which reflect the topology and geometry of some underlying variety. In order to compute these invariants, it is often useful to express the motive of the moduli space in terms of motives of spaces for which the invariants are known. This has been done in some examples for Chow and virtual motives. The origin of such a decomposition of the motive is, in many cases, a Harder-Narasimhan stratification. It is the aim of this project to systematically study such decompositions in Voevodsky's triangulated category of motives which is closely related to motivic homotopy theory, The computation of invariants frequently involves wall-crossing formulae. Recent work of Levine and Pandharipande suggests that such phenomena might be understood in the framework of algebraic cobordism. For this reason, we would like to investigate the relationship between variations of GIT quotients and algebraic cobordism.
DFG Programme
Priority Programmes
International Connection
Ireland, Switzerland
