
TL;DR
This paper develops an intersection theory for difference varieties and introduces the difference Chow form, demonstrating its properties such as transformal homogeneity and order preservation.
Contribution
It presents the first intersection theory for difference varieties and defines the difference Chow form with key properties.
Findings
Intersection of difference varieties with hypersurfaces reduces dimension by one.
Difference Chow form is transformally homogeneous.
Order of the difference Chow form equals the original variety's order.
Abstract
In this paper, the generic intersection theory for difference varieties is presented. Precisely, the intersection of an irreducible difference variety of dimension and order with a generic difference hypersurface of order is shown to be an irreducible difference variety of dimension and order . Based on the intersection theory, the difference Chow form for an irreducible difference variety is defined. Furthermore, it is shown that the difference Chow form of an irreducible difference variety is transformally homogenous and has the same order as .
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory
