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Cohomology of projective space seen by residual complex

Author: I-Chiau Huang
Journal: Trans. Amer. Math. Soc. 353 (2001), 3097-3114
MSC (2000): Primary 14F05, 14F10; Secondary 13N05
Published electronically: March 12, 2001
MathSciNet review: 1828600
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Abstract | References | Similar Articles | Additional Information


A subcomplex of a residual complex on projective space is constructed for computing the cohomology modules of locally free sheaves. A constructive new proof of the Bott formula is given by explicitly exhibiting bases for the cohomology modules.

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  • 1. R. Bott.
    Homogeneous vector bundles.
    Annals of Math., 66:203-248, 1957. MR 19:681d
  • 2. A. Grothendieck.
    The cohomology theory of abstract algebraic varieties.
    In Proc. Internat. Congress Math. (Edinburgh, 1958), pages 103-118. Cambridge University Press, 1960. MR 24:A733
  • 3. R. Hartshorne.
    Residues and Duality, volume 20 of Lecture Notes in Mathematics.
    Springer-Verlag, 1966. MR 36:5145
  • 4. R. Hartshorne.
    Algebraic Geometry.
    Springer-Verlag, 1977. MR 57:3116
  • 5. I-C. Huang.
    An explicit construction of residual complexes.
    Journal of Algebra, 225:698-739, 2000. CMP 2000:09
  • 6. I-C. Huang.
    Pseudofunctors on modules with zero-dimensional support.
    Mem. Amer. Math. Soc., 114(no. 548):xii+53, 1995. MR 95h:13013
  • 7. I-C. Huang.
    A residue map and its applications to some one-dimensional rings.
    Proc. Amer. Math. Soc., 123(8):2369-2372, 1995. MR 95j:13019
  • 8. I-C. Huang.
    Residue theorem via an explicit construction of traces.
    preprint, 1996.
  • 9. I-C. Huang.
    Theory of residues on the projective plane.
    Manuscripta Math., 92(2):259-272, 1997. MR 98a:14027
  • 10. R. Hübl.
    Residues of regular and meromorphic differential forms.
    Math. Ann., 300(4):605-628, 1994. MR 96e:14017
  • 11. J. Lipman and P. Sastry.
    Residues and duality for Cousin complexes.
    preprint, September 21, 1996.
  • 12. P. Sastry.
    Residues and duality for algebraic schemes.
    Compositio Math., 101(2):133-178, 1996. MR 98a:14029
  • 13. P. Sastry and A. Yekutieli.
    On residue complexes, dualizing sheaves and local cohomology modules.
    Israel J. Math., 90:325-348, 1995. MR 96f:14021
  • 14. A. Yekutieli.
    An explicit construction of the Grothendieck residue complex.
    Astérisque 208, 1992.
    With an appendix by Pramathanath Sastry. MR 94e:14026
  • 15. A. Yekutieli.
    Residues and differential operators on schemes.
    Duke Math. J., 95(2):305-341, 1998. MR 99j:14019
  • 16. A. Yekutieli.
    Smooth formal embeddings and the residue complex.
    Canad. J. Math., 50(4):863-896, 1998. MR 99i:14004

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Additional Information

I-Chiau Huang
Affiliation: Institute of Mathematics, Academia Sinica, Nankang, Taipei 11529, Taiwan, R.O.C.

Keywords: Bott formula, injective resolution, residual complex
Received by editor(s): January 10, 2000
Published electronically: March 12, 2001
Article copyright: © Copyright 2001 American Mathematical Society