The Degree and regularity of vanishing ideals of algebraic toric sets over finite fields

Details The Degree and regularity of vanishing ideals of algebraic toric sets over finite fields The Degree and regularity of vanishing ideals of algebraic toric sets over finite fields

2011-10-10

arxiv.org/abs/1110.2124v1

Mathematics

Commutative Algebra

Scientific paper

Let X* be a subset of an affine space A^s, over a finite field K, which is parameterized by the edges of a clutter. Let X and Y be the images of X* under the maps x --> [x] and x --> [(x,1)] respectively, where [x] and [(x,1)] are points in the projective spaces P^{s-1} and P^s respectively. For certain clutters and for connected graphs, we were able to relate the algebraic invariants and properties of the vanishing ideals I(X) and I(Y). In a number of interesting cases, we compute its degree and regularity. For Hamiltonian bipartite graphs, we show the Eisenbud-Goto regularity conjecture. We give optimal bounds for the regularity when the graph is bipartite. It is shown that X* is an affine torus if and only if I(Y) is a complete intersection. We present some applications to coding theory and show some bounds for the minimum distance of parameterized linear codes for connected bipartite graphs.

Affiliated with

Also associated with

No associations

Rating

The Degree and regularity of vanishing ideals of algebraic toric sets over finite fields 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 Degree and regularity of vanishing ideals of algebraic toric sets over finite fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Degree and regularity of vanishing ideals of algebraic toric sets over finite fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-147833