Residues and duality for singularity categories of isolated Gorenstein singularities

Details Residues and duality for singularity categories of isolated Gorenstein singularities Residues and duality for singularity categories of isolated Gorenstein singularities

2009-12-08

arxiv.org/abs/0912.1629v3

Mathematics

Commutative Algebra

28 pages, the exposition has been simplified and shortened

Scientific paper

We study Serre duality in the singularity category of an isolated Gorenstein singularity and find an explicit formula for the duality pairing in terms of generalised fractions and residues. For hypersurfaces we recover the residue formula of the string theorists Kapustin and Li. These results are obtained from an explicit construction of complete injective resolutions of maximal Cohen-Macaulay modules.

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