Kernels for categories of graded singularities

Matthew Ballard, University of Pennsylvania
Fine Hall 322

Due to work of D. Orlov, there is a strong relationship between the derived category of coherent sheaves on a hypersurface in projective space and the category of singularities of the Z-graded affine cone over the hypersurface. For a pair of graded hypersurfaces, I will describe another category of graded singularities which is equivalent to the category of functors between the pair. Combining our construction with Orlov's result and a result of B. Toën provides interesting relationships between the derived categories of some projective varieties. This is joint work with D. Favero and L. Katzarkov.