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Residues and duality for singularity categories of isolated Gorenstein singularities

Part of: Abelian categories Theory of modules and ideals

Published online by Cambridge University Press:  09 September 2013

Daniel Murfet
Daniel Murfet*
Affiliation:
UCLA, Los Angeles, CA 90095-1555, USA email daniel.murfet@math.ucla.edu
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Abstract

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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.

Keywords

singularity categorymaximal Cohen–Macaulay modules

MSC classification

Secondary: 13C14: Cohen-Macaulay modules 18E30: Derived categories, triangulated categories
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 12 , December 2013 , pp. 2071 - 2100
Copyright
© The Author(s) 2013 

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