The projective closure

2001 ◽  
pp. 23-34
Author(s):  
Gerd Fischer
Keyword(s):  
Projective Closure

scholarly journals Parameterized affine codes

2012 ◽  
Vol 49 (3) ◽  
pp. 406-418 ◽  
Author(s):  
Hiram López ◽  
Eliseo Sarmiento ◽  
Maria Pinto ◽  
Rafael Villarreal
Keyword(s):  
Finite Field ◽  
Gröbner Bases ◽  
Algebraic Method ◽  
Grobner Bases ◽  
Projective Closure ◽  
Basic Parameters ◽  
Projective Code ◽  
Vanishing Ideals

Let K be a finite field and let X* be an affine algebraic toric set parameterized by monomials. We give an algebraic method, using Gröbner bases, to compute the length and the dimension of CX* (d), the parameterized affine code of degree d on the set X*. If Y is the projective closure of X*, it is shown that CX* (d) has the same basic parameters that CY (d), the parameterized projective code on the set Y. If X* is an affine torus, we compute the basic parameters of CX* (d). We show how to compute the vanishing ideals of X* and Y.

scholarly journals Equations for the projective closure and effective Nullstellensatz

1991 ◽  
Vol 33 (1-3) ◽  
pp. 11-23 ◽  
Author(s):  
L. Caniglia ◽  
A. Galligo ◽  
J. Heintz
Keyword(s):  
Effective Nullstellensatz ◽  
Projective Closure
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