Felix Küng (University of Liverpool): Twisted Hodge diamonds give rise to non-Fourier-Mukai functors

Second of two lectures on constructing non-Fourier-Mukai functors


We apply computations of twisted Hodge diamonds to construct an infinite number of non-Fourier-Mukai functors. To do this we first recall the construction by Rizzardo, Van den Bergh and Neeman of passing through a non-geometric deformation of a variety along a suitable Hochschild cocycle. We then use twisted Hodge diamonds to control the dimensions of the Hochschild cohomology of hypersurfaces in projective space and prove that there are a large number of Hochschild cohomology classes that allow this type of construction. In particular we can use these calculations to construct non-Fourier-Mukai functors for arbitrary degree hypersurfaces in arbitrary high dimensions.

Published Oct. 11, 2021 11:26 AM - Last modified Oct. 22, 2021 4:23 PM