3,609 research outputs found
A generalized Gaeta's Theorem
We generalize Gaeta's Theorem to the family of determinantal schemes. In
other words, we show that the schemes defined by minors of a fixed size of a
matrix with polynomial entries belong to the same G-biliaison class of a
complete intersection whenever they have maximal possible codimension, given
the size of the matrix and of the minors that define them.Comment: 17 pages, submitte
The G-biliaison class of symmetric determinantal schemes
We consider a family of schemes, that are defined by minors of a homogeneous
symmetric matrix with polynomial entries. We assume that they have maximal
possible codimension, given the size of the matrix and of the minors that
define them. We show that these schemes are G-bilinked to a linear variety of
the same dimension. In particular, they can be obtained from a linear variety
by a finite sequence of ascending G-biliaisons on some determinantal schemes.
In particular, it follows that these schemes are glicci. We describe the
biliaisons explicitely in the proof of the main theorem.Comment: 20 pages, reference addeded, a few mistakes fixed, final version to
appear on J. Algebr
Mixed ladder determinantal varieties from two-sided ladders
We study the family of ideals defined by mixed size minors of two-sided
ladders of indeterminates. We compute their Groebner bases with respect to a
skew-diagonal monomial order, then we use them to compute the height of the
ideals. We show that these ideals correspond to a family of irreducible
projective varieties, that we call mixed ladder determinantal varieties. We
show that these varieties are arithmetically Cohen-Macaulay. We characterize
the arithmetically Gorenstein ones, among those that satisfy a technical
condition. Our main result consists in proving that mixed ladder determinantal
varieties belong to the same G-biliaison class of a linear variety.Comment: 15 pages, contains an improved version of Theorem 1.25 (now 1.23
Partial Spreads in Random Network Coding
Following the approach by R. K\"otter and F. R. Kschischang, we study network
codes as families of k-dimensional linear subspaces of a vector space F_q^n, q
being a prime power and F_q the finite field with q elements. In particular,
following an idea in finite projective geometry, we introduce a class of
network codes which we call "partial spread codes". Partial spread codes
naturally generalize spread codes. In this paper we provide an easy description
of such codes in terms of matrices, discuss their maximality, and provide an
efficient decoding algorithm
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