Finite geometry and the Gale transform

The Gale transform is an involution on sets of points in a projective space. It plays a crucial role in several different subjects, such as algebraic geometry, optimization, coding theory, etc. Sometimes, in the literature, the Gale transform is used implicitly, without mentioning it as such. In the...

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Published inDiscrete mathematics Vol. 310; no. 22; pp. 3206 - 3210
Main Authors Cossidente, Antonio, Sonnino, Angelo
Format Journal Article Conference Proceeding
LanguageEnglish
Published Kidlington Elsevier B.V 28.11.2010
Elsevier
Subjects
Algebra
Algebraic geometry
Cap
Coding
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Functional analysis
Gale transform
Geometry
Mathematical analysis
Mathematics
Optimization
Projective space
Sciences and techniques of general use
Transforms
Gale transform
Cap
Projective space
Coding theory
Optimization method
Discrete mathematics
Combinatorics
Algebraic geometry
Optimization
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ISSN0012-365X
1872-681X
DOI10.1016/j.disc.2009.08.019

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Summary:The Gale transform is an involution on sets of points in a projective space. It plays a crucial role in several different subjects, such as algebraic geometry, optimization, coding theory, etc. Sometimes, in the literature, the Gale transform is used implicitly, without mentioning it as such. In the present paper, we give a short account of the algebraic and geometrical implications that the Gale transform has when it is applied to sets of points in finite projective spaces.
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ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2009.08.019