Abstract:
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.