38 research outputs found
Cayley-Bacharach and evaluation codes on complete intersections
In recent work, J. Hansen uses cohomological methods to find a lower bound
for the minimum distance of an evaluation code determined by a reduced complete
intersection in the projective plane. In this paper, we generalize Hansen's
results from P^2 to P^m; we also show that the hypotheses in Hansen's work may
be weakened. The proof is succinct and follows by combining the
Cayley-Bacharach theorem and bounds on evaluation codes obtained from reduced
zero-schemes.Comment: 10 pages. v2: minor expository change
Complete intersections in binomial and lattice ideals
For the family of graded lattice ideals of dimension 1, we establish a
complete intersection criterion in algebraic and geometric terms. In positive
characteristic, it is shown that all ideals of this family are binomial set
theoretic complete intersections. In characteristic zero, we show that an
arbitrary lattice ideal which is a binomial set theoretic complete intersection
is a complete intersection.Comment: Internat. J. Algebra Comput., to appea
Complete intersection vanishing ideals on degenerate tori over finite fields
We study the complete intersection property and the algebraic invariants
(index of regularity, degree) of vanishing ideals on degenerate tori over
finite fields. We establish a correspondence between vanishing ideals and toric
ideals associated to numerical semigroups. This correspondence is shown to
preserve the complete intersection property, and allows us to use some
available algorithms to determine whether a given vanishing ideal is a complete
intersection. We give formulae for the degree, and for the index of regularity
of a complete intersection in terms of the Frobenius number and the generators
of a numerical semigroup.Comment: Arabian Journal of Mathematics, to appea