Dualization of projective algebraic sets by using Gröbner bases elimination techniques

Details Dualization of projective algebraic sets by using Gröbner bases elimination techniques Dualization of projective algebraic sets by using Gröbner bases elimination techniques

2011-01-13

arxiv.org/abs/1101.2615v1

Mathematics

Algebraic Geometry

16 pages, 7 figures, Singular example code

Scientific paper

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

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