Abstract
We study the components of the Chow variety \({\mathcal {C}}_{1,3}({\mathbb P}^3)\) of 1-cycles of degree 3 in \({\mathbb P}^3\). To do this, we calculate explicit specializations at the components \(H(3,-1),\) and \(H(3,-2)\) of the Hilbert schemes Hilb\(^{3m+2}({\mathbb P}^3)\) and Hilb\(^{3m+3}({\mathbb P}^3)\), respectively. This will give us a partial description of the stratifications of the components \(H(3,-1),\) and \(H(3,-2)\) and, therefore, the birational Hilbert–Chow morphism will give a partial description of the corresponding components of the Chow variety \({\mathcal {C}}_{1,3}({\mathbb P}^3)\).
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I would like to thank the referees for their detailed comments and suggestions that helped to improve the presentation of the results of this paper.
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Piedra, A. A partial description of the Chow variety of 1-cycles of degree 3 in \({\mathbb P}^3\). Bol. Soc. Mat. Mex. 25, 21–51 (2019). https://doi.org/10.1007/s40590-017-0182-6
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DOI: https://doi.org/10.1007/s40590-017-0182-6