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arXiv · 1504.03755

Differential Chow varieties exist

James Freitag·Wei Li·Thomas Scanlon
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Abstract

Chow varieties are a parameter space for cycles of a given variety of a given codimension and degree. We construct their analog for differential algebraic varieties with differential algebraic subvarieties, answering a question of Gao, Li and Wei. The proof uses the construction of classical algebro-geometric Chow varieties, the theory of characteristic sets of differential 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 an appendix by William Johnson.

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James Freitag, Wei Li, Thomas Scanlon. 2015-04-15. Differential Chow varieties exist. https://doi.org/10.1112/jlms.12002

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