Residues and duality for singularity categories of isolated Gorenstein singularities

Preprint English OPEN
Murfet, Daniel;
(2009)
  • Related identifiers: doi: 10.1112/S0010437X13007082
  • Subject: Mathematics - Commutative Algebra | Mathematics - Algebraic Geometry
    arxiv: Mathematics::Commutative Algebra | Mathematics::Category Theory
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 Kapusti... View more
  • References (23)
    23 references, page 1 of 3

    M. R. Douglas, D-Branes, Categories, and N = 1 supersymmetry, J. Math. Phys. 42 (2001) 2818- 2843, arXiv:hep-th/0011017.

    T. Dyckerhoff and D. Murfet, The Kapustin-Li formula revisited, arXiv:1004.0687.

    T. Dyckerhoff and D. Murfet, Pushing forward matrix factorisations, arXiv:1102.2957.

    D. Eisenbud, Homological algebra on a complete intersection, with an application to group representations, Trans. Amer. Math. Soc. 260 (1980), no. 1, 35-64.

    E.E. Enochs and O.M.G. Jenda, Gorenstein injective and projective modules, Math. Z. 220 (1995), no.4, 611-633.

    P. Gabriel, Objets injectifs dans les cat´egories ab´eliennes, S´eminaire P. Dubriel (12e ann´ee 1958/1959), 17-01 to 17-32.

    GLS07 G. M. Greuel, C. Lossen, and E. Shustin, Introduction to singularities and deformations, Springer Monographs in Mathematics, Springer, Berlin, 2007.

    J. Lipman and P. Sastry, Regular differentials and equidimensional scheme-maps, J. Alg. Geom. 1 (1992), 101-130.

    MSV09 M. Mackaay, M. Stoˇsi´c, and P. Vaz, sl(N )-link homology (N > 4) using foams and the Kapustin-Li formula, Geom. Topol. 13 (2009), no. 2, 1075-1128.

    , Triangulated categories, Annals of Mathematics Studies, vol. 148, Princeton University Press, Princeton, NJ, 2001.

  • Metrics
    No metrics available
Share - Bookmark