Positivity of direct image sheaves

Abstract: Positivity properties of direct image sheaves have deep implications in the geometry of families of varieties. For instance, the existence of enough global sections of pushforwards of higher tensors of the relative canonical bundle of a family, puts certain restrictions on the kinds of varieties that can appear on the fibres etc. I will discuss some these positivity properties, especially the ones that come as a generalisation of the Fujita conjecture and its application to the Iitaka conjecture. This is partially a joint work with Takumi Murayama.

algebraic geometry

Audience: researchers in the topic

CMI seminar series

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