Asymptotic behavior of the dimension of the Chow variety

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• 作者：Brian Lehmann<sup>1sup><sup> ; sup><sup>lehmannb@bc.edusup>
• 关键词：Chow variety ; Cycle ; Volume
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：21 February 2017
• 年：2017
• 卷：308
• 期：Complete
• 页码：815-835
• 全文大小：415 K
• 卷排序：308

文摘

First, we calculate the dimension of the Chow variety of degree d cycles on projective space. We show that the component of maximal dimension usually parametrizes degenerate cycles, confirming a conjecture of Eisenbud and Harris. Second, for a numerical class α on an arbitrary variety, we study how the dimension of the components of the Chow variety parametrizing cycles of class mα grows as we increase m. We show that when the maximal growth rate is achieved, α is represented by cycles that are “degenerate” in a precise sense.