publication . Article . Preprint . 2009

Residues and duality for singularity categories of isolated Gorenstein singularities

Daniel Murfet;
Open Access
  • Published: 08 Dec 2009 Journal: Compositio Mathematica, volume 149, pages 2,071-2,100 (issn: 0010-437X, eissn: 1570-5846, Copyright policy)
  • Publisher: Wiley
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.
arXiv: Mathematics::Commutative AlgebraMathematics::Category Theory
free text keywords: Algebra and Number Theory, Mathematics - Commutative Algebra, Mathematics - Algebraic Geometry, Serre duality, Pairing, Pure mathematics, Duality (optimization), Injective function, Singularity theory, Algebra, Singularity, Mathematics, Gravitational singularity
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