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In this note we study standard and good determinantal schemes. We show that there exist arithmetically Cohen-Macaulay schemes that are not standard determinantal, and whose general hyperplane section is good determinantal. We prove that if a general hyperplane section of a scheme is standard (resp. good) determinantal, then the scheme is standard (resp. good) determinantal up to flat deformation. We also study the transfer of the property of being standard or good determinantal under basic double links., 21 pages, the content has been reorganized and there are substantial changes, final version to appear in the proceedings of MAGIC05

In this paper, we discuss some necessary and sufficient condition for a curve to be arithmetically Cohen-Macaulay, in terms of its general hyperplane section. We obtain a characterization of the degree matrices that can occur for points in the plane that are the general hyperplane section of a non arithmetically Cohen-Macaulay curve of P^3. We prove that almost all the degree matrices with positive subdiagonal that occur for the general plane section of a non arithmetically Cohen-Macaulay curve of P^3, arise also as degree matrices of the general plane section of some smooth, integral, non arithmetically Cohen-Macaulay curve, and we characterize the exceptions. We give a necessary condition on the graded Betti numbers of the general hyperplane section of an arithmetically Buchsbaum, (non arithmetically Cohen-Macaulay) curve in P^n. For curves in P^3, we show that any set of Betti numbers that satisfies that condition, can be realised as the Betti numbers of the general plane section of an arithmetically Buchsbaum, non arithmetically Cohen-Macaulay curve. We also show that the matrices that arise as degree matrix of the general plane section of an arithmetically Buchsbaum, integral, (smooth) non arithmetically Cohen-Macaulay space curve are exactly those that arise as degree matrix of the general plane section of an arithmetically Buchsbaum, non arithmetically Cohen-Macaulay space curve and have positive subdiagonal. We also prove some bounds on the dimension of the deficiency module of an arithmetically Buchsbaum space curve, in terms of the degree matrix of the general plane section of the curve., 55 pages, to appear in Transactions AMS

Genetic variation enables both adaptive evolutionary changes and artificial selection. Genetic makeup of populations is the result of a long-term process of selection and adaptation to specific environments and ecosystems. The aim of this study was to characterize the genetic variability of México's chicken population to reveal any underlying population structure. A total of 213 chickens were sampled in different rural production units located in 25 states of México. Genotypes were obtained using the Affymetrix Axiom ® 600 K Chicken Genotyping Array. The Identity by Descent (IBD) and the principal components analysis (PCA) were performed by SVS software on pruned single nucleotide polymorphisms (SNPs). ADMIXTURE analyses identified 3 ancestors and the proportion of the genetic contribution of each of them has been determined in each individual. The results of the Neighbor-Joining (NJ) analysis resulted consistent with those obtained by the PCA. All methods utilized in this study did not allow a classification of Mexican chicken in distinct clusters or groups. A total of 3,059 run of homozygosity (ROH) were identified and, being mainly short in length (

In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size $k\times n$ with entries in a finite field $\mathbb F_q$. Spread codes are a family of optimal codes with maximal minimum distance. We give a minimum-distance decoding algorithm which requires $\mathcal{O}((n-k)k^3)$ operations over an extension field $\mathbb F_{q^k}$. Our algorithm is more efficient than the previous ones in the literature, when the dimension $k$ of the codewords is small with respect to $n$. The decoding algorithm takes advantage of the algebraic structure of the code, and it uses original results on minors of a matrix and on the factorization of polynomials over finite fields.

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., 17 pages, submitted

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., 15 pages, contains an improved version of Theorem 1.25 (now 1.23)

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. Algebra