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In this chapter we give a description of the space of (compact) cycles of dimension n in the complex projective space \(\mathbb {P}_N\) and compare the classical construction of Chow and Van der Warden [C-vW.37] with the general construction given in Chap. 5 . The goal is to show that the reduced complex space underlying the projective variety obtained by the classical algebraic construction is canonically isomorphic to the complex space \(\mathcal {C}_n(\mathbb {P}_N)\) constructed in Chap. 5 .

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Chow Varieties and Cycle Spaces

  • 章节

  • 发表日期：

    2025年

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  • Daniel Barlet,
  • Jón Magnússon

摘要

In this chapter we give a description of the space of (compact) cycles of dimension n in the complex projective space \(\mathbb {P}_N\) and compare the classical construction of Chow and Van der Warden [C-vW.37] with the general construction given in Chap. 5 . The goal is to show that the reduced complex space underlying the projective variety obtained by the classical algebraic construction is canonically isomorphic to the complex space \(\mathcal {C}_n(\mathbb {P}_N)\) constructed in Chap. 5 .