Work

Differential Chow varieties exist

Year: 2016

Type: article

Abstract: The Chow variety is a parameter space for effective algebraic cycles on P n (or A n ) of given dimension and degree. We construct its analog for differential algebraic cycles on A n , 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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.12002

Authors: James Freitag, Wei Li, Thomas Scanlon, William Johnson

Institutions: University of California, Los Angeles, Chinese Academy of Sciences, Academy of Mathematics and Systems Science, University of California, Berkeley

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, National Natural Science Foundation of China

Awards: Model Theory of Generalized Differential Equations and Diophantine Geometry, G5273279963