The aim of this chapter is to prove the existence of a relative fundamental class for an analytic family of cycles in a complex manifold, parameterized by a reduced complex space, and to prove that a family of cycles admits a relative fundamental class if and only if it is analytic. This enables us to define the notion of an analytic family of cycles in a manifold intrinsically, that is to say without referring to local parameterizations.

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Relative Fundamental Classes

  • Daniel Barlet,
  • Jón Magnússon

摘要

The aim of this chapter is to prove the existence of a relative fundamental class for an analytic family of cycles in a complex manifold, parameterized by a reduced complex space, and to prove that a family of cycles admits a relative fundamental class if and only if it is analytic. This enables us to define the notion of an analytic family of cycles in a manifold intrinsically, that is to say without referring to local parameterizations.