ISSN 0253-2778

CN 34-1054/N

Open AccessOpen Access JUSTC Mathematics 19 July 2022

Intersection complex via residues

Cite this:
https://doi.org/10.52396/JUSTC-2021-0263
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  • Author Bio:

    Xiaojin Lin is currently a graduate student under the tutelage of Prof. Mao Sheng at the University of Science and Technology of China. His research interests focus on Hodge theory and vector bundle

  • Corresponding author: E-mail: xjlin@mail.ustc.edu.cn
  • Received Date: 13 December 2021
  • Accepted Date: 10 April 2022
  • Available Online: 19 July 2022
  • We provide an intrinsic algebraic definition of the intersection complex for a variety.
    A normal crossing divisor gives rise to a stratification of a smooth scheme, and a logarithmic connection of a vector bundle along the divisor induces residue maps along each stratums.
    We provide an intrinsic algebraic definition of the intersection complex for a variety.
    • We provide an intrinsic definition of intersection subcomplex via these residues.
    • We present its explicit geometric description.

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  • [1]
    Sheng M, Zhang Z. On the decomposition theorem for intersection de Rham complexes. [2021-11-10]. https://arxiv.org/abs/1904.06651.
    [2]
    Hartshorne R. Algebraic Geometry. Berlin: Springer, 1975.
    [3]
    Schmid W. Variation of Hodge structure: The singularities of the period mapping. Inventiones Mathematicae, 1973, 22 (3): 211–319. doi: 10.1007/BF01389674
    [4]
    Kashiwara M, Kawai T. Poincare lemma for a variation of polarized Hodge structure. In: Hodge Theory. Berlin: Springer, 1987.
    [5]
    Cattani E, Kaplan A, Schmid W. L2 and intersection cohomologies for a polarizable variation of Hodge structure. Inventiones Mathematicae, 1987, 87: 217–252. doi: 10.1007/BF01389415
    [6]
    Peters C, Steenbrink J. Mixed Hodge Structures. Berlin: Springer, 2008.
    [7]
    Voisin C. Hodge Theory and Complex Algebraic Geometry I. Cambridge, UK: Cambridge University Press, 2003.
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Catalog

    [1]
    Sheng M, Zhang Z. On the decomposition theorem for intersection de Rham complexes. [2021-11-10]. https://arxiv.org/abs/1904.06651.
    [2]
    Hartshorne R. Algebraic Geometry. Berlin: Springer, 1975.
    [3]
    Schmid W. Variation of Hodge structure: The singularities of the period mapping. Inventiones Mathematicae, 1973, 22 (3): 211–319. doi: 10.1007/BF01389674
    [4]
    Kashiwara M, Kawai T. Poincare lemma for a variation of polarized Hodge structure. In: Hodge Theory. Berlin: Springer, 1987.
    [5]
    Cattani E, Kaplan A, Schmid W. L2 and intersection cohomologies for a polarizable variation of Hodge structure. Inventiones Mathematicae, 1987, 87: 217–252. doi: 10.1007/BF01389415
    [6]
    Peters C, Steenbrink J. Mixed Hodge Structures. Berlin: Springer, 2008.
    [7]
    Voisin C. Hodge Theory and Complex Algebraic Geometry I. Cambridge, UK: Cambridge University Press, 2003.

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