Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology

Here we study vector bundles $E$ on the Hirzebruch surface $F_e$ such that their twists by a spanned, but not ample, line bundle $M = \mathcal {O}_{F_e}(h+ef)$ have natural cohomology, i.e. $h^0(F_e,E(tM)) >0$ implies $h^1(F_e,E(tM)) = 0$.Comment: 7 pages, no figures, to appear on Cent. Eur. J. Mat

Horrocks Correspondence on a Quadric Surface

We extend the Horrocks correspondence between vector bundles and cohomology modules on the projective plane to the product of two projective lines. We introduce a set of invariants for a vector bundle on the product of two projective lines, which includes the first cohomology module of the bundle, and prove that there is a one to one correspondence between these sets of invariants and isomorphism classes of vector bundles without line bundle summands.Comment: 19 page

Horrocks Correspondence on ACM Varieties

We describe a vector bundle \sE on a smooth $n$-dimensional ACM variety in terms of its cohomological invariants H^i_*(\sE), $1\leq i \leq n-1$, and certain graded modules of "socle elements" built from \sE. In this way we give a generalization of the Horrocks correspondence. We prove existence theorems where we construct vector bundles from these invariants and uniqueness theorems where we show that these data determine a bundle up to isomorphisms. The cases of the quadric hypersurface in $\mathbb P^{n+1}$ and the Veronese surface in $\mathbb P^5$ are considered in more detail.Comment: 18 pages, not figure

Low Rank Vector Bundles on the Grassmannian G(1,4)

Here we define the concept of $L$-regularity for coherent sheaves on the Grassmannian G(1,4) as a generalization of Castelnuovo-Mumford regularity on ${\bf{P}^n}$. In this setting we prove analogs of some classical properties. We use our notion of $L$-regularity in order to prove a splitting criterion for rank 2 vector bundles with only a finite number of vanishing conditions. In the second part we give the classification of rank 2 and rank 3 vector bundles without "inner" cohomology (i.e. H^i_*(E)=H^i(E\otimes\Q)=0 for any $i=2,3,4$) on G(1,4) by studying the associated monads.Comment: 11 pages, no figure

Rank two bundles on P^n with isolated cohomology

The purpose of this paper is to study minimal monads associated to a rank two vector bundle $\mathcal E$ on $\mathbb P^n$. In particular, we study situations where $\mathcal E$ has $H^i_*(\mathcal E) =0$ for $1<i<n-1$, except for one pair of values $(k,n-k)$. We show that on $\mathbb P^8,$ if $H^3_*(\mathcal E)=H^4_*(\mathcal E)=0$, then $\mathcal E$ must be decomposable. More generally, we show that for $n\geq 4k$, there is no indecomposable bundle $\mathcal E$ for which all intermediate cohomology modules except for $H^1_*, H^k_*, H^{n-k}_*, H^{n-1}_*$ are zero.Comment: 14 pages, no figure

Radiosounding: Possible change in aerological data due to instrument change

radiosounding system allows to measure the profile of some meteorological quantities (temperature, humidity, pressure) from the ground up to a certain altitude. Such systems are continuously used by meteorological services in order to perform periodical measurements during the day, at pre-determined times. The evolution of instrumentation technology leads to a fast obsolescence of equipment through time, so that, inevitably, new instrumentation replaces the old one. The new VAISALA Radiosound RS92 has been recently introduced to substitute previous model RS90. The RS90 is currently used by many national and international institutes, including the Italian Air Force Meteorological Service (Servizio Meteorologico dell’Aeronautica Militare). In order to assess the way in which the substitution of RS90s with the new RS92s would affect measures performed by the altitude observation network with regard also to the historical series, several comparative measurements have been conducted by the “Reparto Sperimentazioni di Meteorologia Aeronautica” at Vigna di Valle (Rome). During this testing series, Company VAISALA has given a remarkable level of cooperation by a continuous presence of technicians. The entire test has been performed according to WMO (World Meteorological Organization) protocols

Spacecraft charging and ion wake formation in the near-Sun environment

A three-dimensional (3-D), self-consistent code is employed to solve for the static potential structure surrounding a spacecraft in a high photoelectron environment. The numerical solutions show that, under certain conditions, a spacecraft can take on a negative potential in spite of strong photoelectron currents. The negative potential is due to an electrostatic barrier near the surface of the spacecraft that can reflect a large fraction of the photoelectron flux back to the spacecraft. This electrostatic barrier forms if (1) the photoelectron density at the surface of the spacecraft greatly exceeds the ambient plasma density, (2) the spacecraft size is significantly larger than local Debye length of the photoelectrons, and (3) the thermal electron energy is much larger than the characteristic energy of the escaping photoelectrons. All of these conditions are present near the Sun. The numerical solutions also show that the spacecraft's negative potential can be amplified by an ion wake. The negative potential of the ion wake prevents secondary electrons from escaping the part of spacecraft in contact with the wake. These findings may be important for future spacecraft missions that go nearer to the Sun, such as Solar Orbiter and Solar Probe Plus.Comment: 25 pages, 7 figures, accepted for publication in Physics of Plasma