Dualization of projective algebraic sets by using Gr\"obner bases elimination techniques
Algebraic Geometry
2011-01-14 v1 Commutative Algebra
Abstract
The set of common roots of a finite set (it is an ideal) of homogeneous polynomials is known as projective algebraic set . In this article I show how to dualize such projective algebraic sets by elimination of variables from a system of polynomials with the Gr\"obner bases method. A dualization algorithm is implemented in the computer algebra system {\sc Singular}. Some examples are given. The main diagram shows the relationship between the ideal , its radical and their dual ideals.
Cite
@article{arxiv.1101.2615,
title = {Dualization of projective algebraic sets by using Gr\"obner bases elimination techniques},
author = {Călin-Şerban Bărbat},
journal= {arXiv preprint arXiv:1101.2615},
year = {2011}
}
Comments
16 pages, 7 figures, Singular example code