Title: Optimal symplectic connections on holomorphic submersions
2019.09.13 |
Date | Wed 18 Sep |
Time | 16:15 — 17:15 |
Location | Aud-D3 (1531-215) |
Abstract:
An important question in Kähler geometry is the existence question for canonical metrics. In this talk I will discuss a construction producing such metrics on the total space of fibrations with cscK fibres, in certain "adiabatic" classes where the fibres are small. Such constructions have a rich history going back to the work of Fine, Hong and others. The situation gets more complicated in the presence of automorphisms. I will discuss an equation that we call the optimal symplectic connection equation, that conjecturally determines a canonical choice of fibrewise cscK metrics when the fibres have automorphisms. Assuming the existence of a solution to this equation, we show that the desired metrics on the total space can be constructed. This is joint work with Ruadhaí Dervan.