Mathematische Annalen

, Volume 237, Issue 1, pp 41–77

Duality and intersection theory in complex manifolds. I

  • Domingo Toledo
  • Yue Lin L. Tong
Article

DOI: 10.1007/BF01351557

Cite this article as:
Toledo, D. & Tong, Y.L.L. Math. Ann. (1978) 237: 41. doi:10.1007/BF01351557

Abstract

We introduce the concept of a twisting cochain and a twisted complex associated to a coherent sheaf. For sheaves of submanifolds these twisted complexes are used to construct on cochain level the Grothendieck theory of dual class and Gysin map. These explicit constructions give, for instance, a local formula for dual class of higher codimensional submanifolds. We prove a refined version of the Hirzebruch Riemann Roch using such local formulas. We also prove a theorem on when global analytic intersection classes can be computed from first order geometric data. This theory will be used to prove the Holomorphic Lefschetz formula (in Part II) and the Hirzebruch Riemann Roch for analytic coherent sheaves.

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Domingo Toledo
    • 1
    • 2
  • Yue Lin L. Tong
    • 1
    • 2
  1. 1.Columbia UniversityUSA
  2. 2.Purdue UniversityUSA

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