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We study Serre duality in the singularity category of an isolated Gorensteinsingularity and find an explicit formula for the duality pairing in terms ofgeneralised fractions and residues. For hypersurfaces we recover the residueformula of the string theorists Kapustin and Li. These results are obtainedfrom an explicit construction of complete injective resolutions of maximalCohen-Macaulay modules.

Residues and duality for singularity categories of isolated Gorenstein singularities