Optimal symplectic connections on holomorphic submersions
Lars Martin Sektnan
Onsdag 18. september 2019
Aud. D3 (1531-215)
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.
Kontakt: Cristiano Spotti