We describe a technique which permits a uniform construction of a number of low rank bundles, both known and new. In characteristic two, we obtain rank two bundles on P5. In characteristic p, we obtain rank two bundles on P4 and rank three bundles on P5. In arbitrary characteristic, we obtain rank three bundles on P4 and rank two bundles on the quadric S5 in P6.

Combinatorial vector bundles, or matroid bundles, are a combinatorial analog to real vector bundles. Combinatorial objects called oriented matroids play the role of real vector spaces. This combinatorial analogy is remarkably strong, and has led to combinatorial results in topology and bundle-theoretic proofs in combinatorics. This paper surveys recent results on matroid bundles, and describes ...

Any line bundle L on a smooth curve C of genus g with degL ≥ 2g+1 is normally generated, i.e., φL(C) ⊆ PH(C,L) is projectively normal. However, it has known that more various line bundles of degree d failing to be normally generated appear on multiple coverings of genus g as d becomes smaller than 2g+1. Thus, investigating the normal generation of line bundles on multiple coverings can be an ef...

This paper studies Kontsevich’s characteristic classes of smooth bundles with fiber a ‘singularly’ framed odd-dimensional homology sphere which are defined through his graph complex and configuration space integral. We will give a systematic construction of smooth bundles parametrized by trivalent graphs and will show that our smooth bundles are nontrivially detected by Kontsevich’s characteris...

It is known that to every (1|1)-dimensional supercurve X there is associated a dual supercurve X̂ , and a superdiagonal∆ ⊂ X× X̂ . We establish that the categories ofD-modules on X , X̂ and ∆ are equivalent. This follows from a more general result aboutD-modules and purely odd submersions. The equivalences preserve tensor products, and take vector bundles to vector bundles. Line bundles with conne...

In this paper we propose a novel approach for the systematic assessment and analysis of IT related risks in organisations and projects. The approach is model-driven using an enterprise architecture as the basis for the security management process. Using an enterprise architecture it is possible to provide an integrated description of an organisation’s structure, processes and its underlying IT ...

IT risk management is an important challenge for businesses and software vulnerabilities are a major source of IT risks, as the 2006 CSI/FBI Computer Crime and Security Survey [GLLR06] demonstrates. According to the survey, many companies consider it important to quantify the losses attacks against their IT systems cause but are unable to do so. In service-oriented architectures, we see a promi...

The arrangement of vascular bundles in the stems of monocots has been described repeatedly as "scattered." But to the trained eye it is clearly ordered as verified by the use of the R index of Clark and Evans. The arrangement of bundles in leaves and sclerenchyma bundles in stems are also ordered. An equation was developed for the probability distribution frequencies (pdf) for leaf intervein di...

We construct a Petersson-Weil type Kähler form on the moduli spaces of Higgs bundles over a compact Kähler manifold. A fiber integral formula for this form is proved, from which it follows that the Petersson-Weil form is the curvature of a certain determinant line bundle, equipped with a Quillen metric, on the moduli space of Higgs bundles over a projective manifold. The curvature of the Peters...

It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of quantum spaces noncommutative principal and vector bundles are defined and their properties are studied. Important constructions in the classical theory of prin...