Rank 2 stable vector bundles on Fano 3-folds of index 2

AbstractLet X be a Fano 3-fold of the first kind with index 2. In this paper, we characterize the chern classes of rank 2 stable vector bundles on X and we find a bound for the least twist of a rank 2 reflexive sheaf on X which has a global section

A lower bound for the number of components of the moduli schemes of stable rank 2 vector bundles on projective 3-folds

Fix a smooth projective 3-fold X, c1, H ∈ Pic(X) with H ample, and d ∈ Z. Assume the existence of integers a, b with a ≠ 0 such that ac1 is numerically equivalent to bH. Let M(X, 2, c1, d, H) be the moduli scheme of H-stable rank 2 vector bundles, E, on X with c1(E) = c1 and c2(E) · H = d. Let m(X, 2, c1, d, H) be the number of its irreducible components. Then lim supd→ ∞m(X, 2, c1, d, H) = +∞

Altered Metabolic Profile in Congenital Lung Lesions Revealed by1H Nuclear Magnetic Resonance Spectroscopy

Congenital lung lesions are highly complex with respect to pathogenesis and treatment. Large-scale analytical methods, like metabolomics, are now available to identify biomarkers of pathological phenotypes and to facilitate clinical management. Nuclear magnetic resonance (NMR) is a unique tool for translational research, as in vitro results can be potentially translated into in vivo magnetic resonance protocols. Three surgical biopsies, from congenital lung malformations, were analyzed in comparison with one control sample. Extracted hydrophilic metabolites were submitted to high resolution 1H NMR spectroscopy and the relative concentration of 12 metabolites was estimated. In addition, two-dimensional NMR measurements were performed to complement the results obtained from standard monodimensional experiments. This is one of the first reports of in vitro metabolic profiling of congenital lung malformation. Preliminary data on a small set of samples highlights some altered metabolic ratios, dealing with the glucose conversion to lactate, to the relative concentration of phosphatidylcholine precursors, and to the presence of myoinositol. Interestingly some relations between congenital lung lesions and cancer metabolic alterations are found

Decomposition of homogeneous polynomials with low rank

Let $F$ be a homogeneous polynomial of degree $d$ in $m+1$ variables defined over an algebraically closed field of characteristic zero and suppose that $F$ belongs to the $s$-th secant varieties of the standard Veronese variety $X_{m,d}\subset \mathbb{P}^{{m+d\choose d}-1}$ but that its minimal decomposition as a sum of $d$-th powers of linear forms $M_1, ..., M_r$ is $F=M_1^d+... + M_r^d$ with $r>s$. We show that if $s+r\leq 2d+1$ then such a decomposition of $F$ can be split in two parts: one of them is made by linear forms that can be written using only two variables, the other part is uniquely determined once one has fixed the first part. We also obtain a uniqueness theorem for the minimal decomposition of $F$ if the rank is at most $d$ and a mild condition is satisfied.Comment: final version. Math. Z. (to appear

Curve classes on irreducible holomorphic symplectic varieties

We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of K3 type and of Generalized Kummer type. As an application, we give a new proof of the integral Hodge conjecture for cubic fourfolds.Comment: 15 page

On Buchsbaum bundles on quadric hypersurfaces

Let $E$ be an indecomposable rank two vector bundle on the projective space \PP^n, n \ge 3, over an algebraically closed field of characteristic zero. It is well known that $E$ is arithmetically Buchsbaum if and only if $n=3$ and $E$ is a null-correlation bundle. In the present paper we establish an analogous result for rank two indecomposable arithmetically Buchsbaum vector bundles on the smooth quadric hypersurface Q_n\subset\PP^{n+1}, $n\ge 3$. We give in fact a full classification and prove that $n$ must be at most 5. As to $k$-Buchsbaum rank two vector bundles on $Q_3$, $k\ge2$, we prove two boundedness results.Comment: 22 pages, no figur

Thermal Conductivity of Graphite Felt at High Temperatures

Thermal conductivity measurements in vacuum, helium and air of WDF graphite felt were conducted at room temperature. It was found that conduction along the solid paths, gas conduction and radiation between fibres are the dominant heat transfer mechanisms. All heat transfer models reviewed indicated that there are geometrical parameters to be determined experimentally in order to be able to quantify the conduction and radiative mechanisms. Experimental results obtained at room temperature were used to calculate the conduction tortuosity, Ï. Results from the literature were used to determine the radiation constant, Cfr. Using these parameters, an equation for the felt thermal conductivity as a function of the absolute temperature was obtained

Metabolomic profile of amniotic fluid to evaluate lung maturity: the diaphragmatic hernia lamb model

Background: Tracheal occlusion (TO) stimulates lung growth in fetuses affected with congenital diaphragmatic hernia (CDH) although the processes involved in lung maturation still remain unknown. The objective of this study was to evaluate the metabolomic profile of amniotic fluid (AF) following TO in fetal lamb model in order to obtain an indirect view of mechanisms involved in pulmonary reversal hypoplasia and biochemical maturity in response to fetal TO. Methods: Liquid Chromatography Mass Spectrometry was performed on lamb AF samples at: age I (70 days' gestation); age II (102 days' gestation); age III (136 days' gestation). CDH was induced at age I and TO at age II. Results: Betaine, choline, creatinine were found significantly increased during gestation in the control group. The CDH group showed choline (p =0.007) and creatinine (p =0.004) decreases during pregnancy. In the TO group choline and creatinine profiles were restored. Conclusions: Alveolar tissue and fetal global growth ameliorated after TO. Metabolomics provided usefu information on biochemical details during lung maturation. Metabolomic profiling would help to identify the best time to perform TO, in order to increase survival of CDH affected patients

On rationality of the intersection points of a line with a plane quartic

We study the rationality of the intersection points of certain lines and smooth plane quartics C defined over F_q. For q \geq 127, we prove the existence of a line such that the intersection points with C are all rational. Using another approach, we further prove the existence of a tangent line with the same property as soon as the characteristic of F_q is different from 2 and q \geq 66^2+1. Finally, we study the probability of the existence of a rational flex on C and exhibit a curious behavior when the characteristic of F_q is equal to 3.Comment: 17 pages. Theorem 2 now includes the characteristic 2 case; Conjecture 1 from the previous version is proved wron