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This chapter is devoted to the construction, for a given complex space M and a non-negative integer n, of a complex structure of a reduced complex space on the set \(\mathcal {C}_n(M)\) of compact n-dimensional cycles, such that the tautological family parameterized by \(\mathcal {C}_n(M)\) becomes a universal proper analytic family of compact n-cycles in M.

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Construction of the Cycle Space

  • 章节

  • 发表日期：

    2025年

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  • Daniel Barlet,
  • Jón Magnússon

摘要

This chapter is devoted to the construction, for a given complex space M and a non-negative integer n, of a complex structure of a reduced complex space on the set \(\mathcal {C}_n(M)\) of compact n-dimensional cycles, such that the tautological family parameterized by \(\mathcal {C}_n(M)\) becomes a universal proper analytic family of compact n-cycles in M.