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In Chap. 6 we introduced the notion of fundamental class of a cycle in a pure dimensional complex manifold. Moreover, we proved that a family of cycles in a complex manifold is analytic if and only if it admits a relative fundamental class. This shows that the existence of a relative fundamental class characterizes the analytic variation of a family of cycles in a complex manifold. It is interesting to point out that the analyticity of a family of cycles is local and stable by closed embeddings so this characterization can be used (locally) in any ambient space.

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Holomorphic Currents and Intersection Theory on a Nearly Smooth Complex Space

  • 章节

  • 发表日期：

    2025年

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  • Daniel Barlet,
  • Jón Magnússon

摘要

In Chap. 6 we introduced the notion of fundamental class of a cycle in a pure dimensional complex manifold. Moreover, we proved that a family of cycles in a complex manifold is analytic if and only if it admits a relative fundamental class. This shows that the existence of a relative fundamental class characterizes the analytic variation of a family of cycles in a complex manifold. It is interesting to point out that the analyticity of a family of cycles is local and stable by closed embeddings so this characterization can be used (locally) in any ambient space.