English

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 II (it is an ideal) of homogeneous polynomials is known as projective algebraic set VV. In this article I show how to dualize such projective algebraic sets VV 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 II, its radical I\sqrt{I} and their dual ideals.

Keywords

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

R2 v1 2026-06-21T17:11:35.541Z