The Projective Geometry of the Gale Transform

Details The Projective Geometry of the Gale Transform The Projective Geometry of the Gale Transform

1998-07-23

arxiv.org/abs/math/9807127v1

Mathematics

Algebraic Geometry

43 pages, Plain Tex, uses diagrams.tex. Postscript file also available from http://www.math.columbia.edu/~psorin

Scientific paper

The Gale transform, an involution on sets of points in projective space, appears in a multitude of guises, in subjects as diverse as optimization, coding theory, theta-functions, and recently in our proof that certain general sets of points fail to satisfy the minimal free resolution conjecture. In this paper we reexamine the Gale transform in the light of modern algebraic geometry. We give a more general definition, in the context of finite (locally) Gorenstein subschemes. We put in modern form a number of the more remarkable examples discovered in the past, and we add new constructions and connections to other areas of algebraic geometry. We generalize Goppa's theorem in coding theory and we give new applications to Castelnuovo theory. We give references to classical and modern sources.

Affiliated with

Also associated with

No associations

Rating

The Projective Geometry of the Gale Transform does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Projective Geometry of the Gale Transform, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Projective Geometry of the Gale Transform will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-38824