Cokernel bundles and Fibonacci bundles

We are interested in those bundles $C$ on $\mathbb{P}^N$ which admit a resolution of the form $$0 \to \mathbb{C}^s \otimes E \xrightarrow{\mu} \mathbb{C}^t \otimes F \to C \to 0.$$ In this paper we prove that, under suitable conditions on $(E,F)$, a generic bundle with this form is either simple or canonically decomposable. As applications we provide an easy criterion for the stability of such bundles on $\mathbb{P}^2$ and we prove the stability when $E = \mathcal{O}$, $F = \mathcal{O}(1)$ and $C$ is an exceptional bundle on $\mathbb{P}^N$ for $N \geq 2$.Comment: 23 pages, 1 figure, revised version, to appear in Mathematische Nachrichte

Simplicity of generic Steiner bundles

We prove that a generic Steiner bundle E is simple if and only if the Euler characteristic of the endomorphism bundle of E is less or equal to 1. In particular we show that either E is exceptional or it satisfies the following inequality t\leq(\frac{n+1+\sqrt((n+1)^2-4)}{2})s.Comment: 11 page

Semistability of certain bundles on a quintic Calabi-Yau threefold

In the paper ``Chirality change in string theory'', by Douglas and Zhou, the authors give a list of bundles on a quintic Calabi-Yau threefold. Here we prove the semistability of most of these bundles. This provides examples of string theory compactifications which have a different number of generations and can be connected

On the Alexander-Hirschowitz Theorem

The Alexander-Hirschowitz theorem says that a general collection of $k$ double points in ${\bf P}^n$ imposes independent conditions on homogeneous polynomials of degree $d$ with a well known list of exceptions. Alexander and Hirschowitz completed its proof in 1995, solving a long standing classical problem, connected with the Waring problem for polynomials. We expose a self-contained proof based mainly on previous works by Terracini, Hirschowitz, Alexander and Chandler, with a few simplifications. We claim originality only in the case $d=3$, where our proof is shorter. We end with an account of the history of the work on this problem.Comment: 29 pages, the proof in the case of cubics has been simplified, three references added, to appear in J. Pure Appl. Algebr

α_S1-casein in goat milk: identification of genetic variants by Capillary Zone Electrophoresis compared to Isoelectric Focusing

AlphaS1 casein fraction in caprine milk is characterized by an important polymorphism due to substitution, deletion of amino acids and post trascriptional modifications (Grosclaude et al., 1994; Ferranti et al., 1997). This structural polymorphism is associated to a quantitative variability in protein expression related to different milk quality and dairy properties (Pierre et al., 1998; Remeuf, 1993; Vassal et al., 1994). Classical electrophoretic methods were applied to characterize the phenotypic variants at αS1-casein fraction (Addeo et al., 1988; Russo et al., 1986). During the last ten years capillary electrophoresis became an analytical technique for rapid and automated analysis requiring small sample volume and small solvent waste. These characteristics, together with the high resolution and the chance to give quantitative results, made this technique a useful tool in studying milk protein characterization and in detecting adulteration (Cattaneo et al., 1996a; 1996b) in different application fields. CZE was applied to the study of caprine milk proteins to quantify high, medium and low αS1- casein content and to identify genetic variants αS1 A, B and C on the basis of their different migration time (Recio et al., 1997). The aim of this work was to test a CZE procedure able to identify and discriminate the main αS1 caprine variants A, B, E and F through specific and repeatable electromigration patterns. Comparison between CZE and IEF assays is discussed

On a notion of speciality of linear systems in P^n

Given a linear system in P^n with assigned multiple general points we compute the cohomology groups of its strict transforms via the blow-up of its linear base locus. This leads us to give a new definition of expected dimension of a linear system, which takes into account the contribution of the linear base locus, and thus to introduce the notion of linear speciality. We investigate such a notion giving sufficient conditions for a linear system to be linearly non-special for arbitrary number of points, and necessary conditions for small numbers of points.Comment: 26 pages. Minor changes, Definition 3.2 slightly extended. Accepted for publication in Transactions of AM