Differential Chow varieties exist
Differential Chow varieties exist
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DOI：
10.1112/jlms.12002
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发表时间：
2015-04
期刊：
影响因子：
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通讯作者：
J. Freitag;Wei Li-;T. Scanlon;Will Johnson
中科院分区：
文献类型：
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作者：
J. Freitag;Wei Li-;T. Scanlon;Will Johnson
Chow簇是Pn（或An）上给定维数和次数的有效代数圈的参数空间。我们构造了An上的微分代数圈的类似物，回答了Gao，Li和Yuan的问题[Trans.Amer.Math.Soc.365（2013）4575-4632]。证明使用了经典代数几何Chow簇的构造、微分簇和代数簇的特征集理论、延拓空间理论和微分Chow形式理论。在证明过程中，需要代数闭域理论的几个可定义性结果。这些结果的初等证明在附录中给出。
The Chow variety is a parameter space for effective algebraic cycles on Pn (or An ) of given dimension and degree. We construct its analog for differential algebraic cycles on An , answering a question of Gao, Li and Yuan [Trans. Amer. Math. Soc. 365 (2013) 4575–4632]. The proof uses the construction of classical algebro‐geometric Chow varieties, the theory of characteristic sets of differential varieties and algebraic varieties, the theory of prolongation spaces and the theory of differential Chow forms. In the course of the proof, several definability results from the theory of algebraically closed fields are required. Elementary proofs of these results are given in the appendix.