Talk page
Title:
Stability of fibrations
Speaker:
Abstract:
I will describe an analogue of K-stability for fibrations. The notion generalises K-stability of polarised varieties when the base of the fibration is a point, and slope stability of a vector bundle when the fibration is the projectivisation of a vector bundle. Conjecturally, this notion of stability should allow one to form moduli spaces of stable fibrations over a fixed base, and should be equivalent to the existence of certain canonical metrics. These conjectures are analogues of central conjectures in the theory of polarised varieties and vector bundles (essentially all proven for bundles and Fano varieties). The main result will prove one direction of our conjecture linking stability of fibration with the existence of appropriate canonical metrics, which we call "optimal symplectic connections". This is joint work with Lars Sektnan.
Link:
Workshop: