Seminar Algebra and Geometry: Andrea Fanelli (Basel)

On the fibres of Mori fibre spaces

In this talk I will give a fast introduction to the problem of birational classification of algebraic varieties, where Mori fibre spaces naturally appear. I will then discuss a classification project of the Fano varieties which can appear as a general fibre of a Mori fibre space (fibre-like Fano varieties). At this stage we have two criteria, one sufficient and one necessary, to detect the fibre-likeness of a Fano variety. These criteria turn into a characterisation in the rigid case. Our main applications are for surfaces, three-folds and toric varieties.

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