Ulrich bundles on a general blow–up of the plane

We prove that on Xn, the plane blown–up at n general points, there are Ulrich line bundles with respect to a line bundle corresponding to curves of degree m passing simply through the n blown–up points, with m less than or equal to 2 times the square root of n 2, and such that the line bundle in question is very ample on Xn. We prove that the number of these Ulrich line bundles tends to infinity with n. We also prove the existence of slope–stable rank–r Ulrich vector bundles on Xn, for n > 2 and any r > 1 and we compute the dimensions of their moduli spaces. These computations imply that Xn is Ulrich wil

Macht und Gegenmacht im globalen Zeitalter

Ressenya de: Bech, Ulrich: Macht und Gegenmacht im globalen Zeitalter. Frankfurt a. M.: Suhrkamp, 2002

A note on some moduli spaces of Ulrich bundles

We prove that the modular component M(r), constructed in the Main Theorem of a former paper of us (published in Adv. Math on 2024), paramatrizing (isomorphism classes of) Ulrich vector bundles of rank r and given Chern classes, on suitable 3-fold scrolls Xe over Hirzebruch surfaces Fe≥0, which arise as tautological embeddings of projectivization of very-ample vector bundles on Fe, is generically smooth and unirational. A stronger result holds for the suitable associated moduli space MFe(r) of vector bundles of rank r and given Chern classes on Fe, Ulrich w.r.t. the very ample polarization c1(Ee)=OFe(3,be), which turns out to be generically smooth, irreducible and unirational

ACM bundles on cubic surfaces

In this paper we prove that, for every $r \geq 2$, the moduli space $M^s_X(r;c_1,c_2)$ of rank $r$ stable vector bundles with Chern classes $c_1=rH$ and $c_2=(3r^2-r)/2$ on a nonsingular cubic surface $X \subset \mathbb{P}^3$ contains a nonempty smooth open subset formed by ACM bundles, i.e. vector bundles with no intermediate cohomology. The bundles we consider for this study are extremal for the number of generators of the corresponding module (these are known as Ulrich bundles), so we also prove the existence of indecomposable Ulrich bundles of arbitrarily high rank on $X$.Comment: 25 pages, no figures, references added, Example 3.8 extende

Modern optical astronomy: technology and impact of interferometry

The present `state of the art' and the path to future progress in high spatial resolution imaging interferometry is reviewed. The review begins with a treatment of the fundamentals of stellar optical interferometry, the origin, properties, optical effects of turbulence in the Earth's atmosphere, the passive methods that are applied on a single telescope to overcome atmospheric image degradation such as speckle interferometry, and various other techniques. These topics include differential speckle interferometry, speckle spectroscopy and polarimetry, phase diversity, wavefront shearing interferometry, phase-closure methods, dark speckle imaging, as well as the limitations imposed by the detectors on the performance of speckle imaging. A brief account is given of the technological innovation of adaptive-optics (AO) to compensate such atmospheric effects on the image in real time. A major advancement involves the transition from single-aperture to the dilute-aperture interferometry using multiple telescopes. Therefore, the review deals with recent developments involving ground-based, and space-based optical arrays. Emphasis is placed on the problems specific to delay-lines, beam recombination, polarization, dispersion, fringe-tracking, bootstrapping, coherencing and cophasing, and recovery of the visibility functions. The role of AO in enhancing visibilities is also discussed. The applications of interferometry, such as imaging, astrometry, and nulling are described. The mathematical intricacies of the various `post-detection' image-processing techniques are examined critically. The review concludes with a discussion of the astrophysical importance and the perspectives of interferometry.Comment: 65 pages LaTeX file including 23 figures. Reviews of Modern Physics, 2002, to appear in April issu

Key Notes: The Newsletter of the Department of Music

Witch Hunt by Ulrich Schltheiss 20th Anniversary Arranged for Saxophones & Percussion Dr. Ben Warsaw Bach Ascending PERCUSSION ALUMNI PERFORMANCE GUEST ARTIST Graham Spice GUEST ARTIST & GEORGIA SOUTHERN UNIVERSITY Double Alumni Eddie Farr GUEST ARTIST Elainie Lollios GUEST LECTURE Matthew Walker, Owner of M & W Custom Trombones GUEST LECTURE Jeff Clark Student Performance