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Special metrics on fibrations and the optimal symplectic connection

Annamaria Ortu
Thursday, November 5, 2020 - 14:30
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Consider a holomorphic fibration over a Kähler manifold, where all the fibres are constant scalar curvature Kähler manifolds. We will discuss the problem of finding a constant scalar curvature Kähler (cscK) metric on the total space itself. The problem goes back to Hong (1999), who considered the projectivization of a vector bundle over a Kähler manifold: in this case, if the vector bundle admits a Hermite-Einsten structure, then it is possibile to constructs a cscK metric on its projectivization. In this talk, we will present a more general condition, the optimal symplectic connection condition, which gives an analogous result in the full general case, due to R. Dervan and L. M. Sektnan.

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