Translates of Polynomials
Shreeram S. Abhyankar, William J. Heinzer, Avinash Sathaye
TL;DR
This paper investigates the properties of polynomial translates in algebraic geometry, focusing on the behavior of hypersurfaces under translation in affine space over a field.
Contribution
It introduces a new perspective on polynomial translates and analyzes their geometric and algebraic properties in the context of hypersurfaces.
Findings
Characterization of hypersurfaces under polynomial translation
Identification of invariants preserved by translation
Insights into the structure of polynomial families in affine space
Abstract
Let f = 0 be a hypersurface in n-dimensional affine space over a field k. We consider the pencil of hypersurfaces f- c = 0 with c varying over k.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Advanced Differential Equations and Dynamical Systems